@book{AST_2001__273__R1_0, author = {Nishiyama, Kyo and Ochiai, Hiroyuki and Taniguchi, Kenji and Yamashita, Hiroshi and Kato, Shohei}, title = {Nilpotent orbits, associated cycles and {Whittaker} models for highest weight representations}, series = {Ast\'erisque}, publisher = {Soci\'et\'e math\'ematique de France}, number = {273}, year = {2001}, mrnumber = {1845713}, zbl = {0968.22001}, language = {en}, url = {http://archive.numdam.org/item/AST_2001__273__R1_0/} }

TY - BOOK AU - Nishiyama, Kyo AU - Ochiai, Hiroyuki AU - Taniguchi, Kenji AU - Yamashita, Hiroshi AU - Kato, Shohei TI - Nilpotent orbits, associated cycles and Whittaker models for highest weight representations T3 - Astérisque PY - 2001 IS - 273 PB - Société mathématique de France UR - http://archive.numdam.org/item/AST_2001__273__R1_0/ LA - en ID - AST_2001__273__R1_0 ER -

%0 Book %A Nishiyama, Kyo %A Ochiai, Hiroyuki %A Taniguchi, Kenji %A Yamashita, Hiroshi %A Kato, Shohei %T Nilpotent orbits, associated cycles and Whittaker models for highest weight representations %S Astérisque %D 2001 %N 273 %I Société mathématique de France %U http://archive.numdam.org/item/AST_2001__273__R1_0/ %G en %F AST_2001__273__R1_0

Nishiyama, Kyo; Ochiai, Hiroyuki; Taniguchi, Kenji; Yamashita, Hiroshi; Kato, Shohei. Nilpotent orbits, associated cycles and Whittaker models for highest weight representations. Astérisque, no. 273 (2001), 169 p. http://numdam.org/item/AST_2001__273__R1_0/

[NOT] Bernstein degree and associated cycles of Harish-Chandra modules - Hermitian symmetric case -. In this volume. | Zbl

, and ,[Y] Cayley transform and generalized Whittaker models for irreducible highest weight modules. In this volume. | Zbl

,[KO] The degrees of orbits of the multiplicity-free actions. In this volume. | Zbl

and ,[1] The local structure of characters, J. Funct. Anal. 37 (1980), no. 1, 27-55. | MR | Zbl | DOI

and , Jr.,[2] Differential operators and highest weight representations, Mem. Amer. Math. Soc. 94 (1991), no. 455, iv+102 pp. | MR | Zbl

, and ,[3] A classification of unitary highest weight modules, in Representation theory of reductive groups (Park City, Utah, 1982), 97-143, | MR | Zbl

, and ,A classification of unitary highest weight modules Progr. Math., 40, Birkhäuser, Boston, Boston, Mass., 1983. | MR | Zbl

, and ,[4] Intersection theory, Springer, Berlin, 1984. | MR | Zbl | DOI

,[5] Associated variety, Kostant-Sekiguchi correspondence, and locally free $U\left(n\right)$-action on Harish-Chandra modules. J. Math. Soc. Japan 51 (1999), no. 1, 129-149. | MR | Zbl | DOI

and ,[6] Algebraic geometry, A first course. Corrected reprint of the 1992 original, Springer, New York, 1995. | MR

,[7] Some remarks on nilpotent orbits. J. Algebra, 64 (1980), 190-213. | MR | Zbl | DOI

,[8] The Selberg-Jack symmetric functions. Adv. Math., 130 (1997), 33-102. | MR | Zbl | DOI

,[9] Generalized Gel'fand-Graev representations and Ennola duality, in Algebraic groups and related topics (Kyoto/Nagoya, 1983), 175-206 Adv. Stud. Pure Math., 6, North-Holland, Amsterdam-New York, 1985. | MR | Zbl | DOI

,[10] On the Segal-Shale-Weil representations and harmonic polynomials, Invent. Math. 44 (1978), no. 1, 1-47. | MR | Zbl | EuDML | DOI

and ,[11] Whittaker vectors and associated varieties. Invent. Math. 89 (1987), no. 1, 219-224. | MR | Zbl | EuDML | DOI

,[12] ${C}^{-\infty}$ -Whittaker vectors for complex semisimple Lie groups, wave front sets, and Goldie rank polynomial representations, Ann. Sci. Éc. Norm. Sup. 23 (1990), 311-367. | MR | Zbl | EuDML | Numdam | DOI

,[13] Bernstein degree of singular unitary highest weight representations of the metaplectic group. Proc. Japan Acad., 75, Ser. A (1999), 9-11. | MR | Zbl | DOI

and ,[14] Picard-Lefschetz theory and characters of a semisimple Lie group, Invent. Math. 121 (1995), 579-611. | MR | Zbl | EuDML | DOI

,[15] On the stability of branching coefficients of rational representations of reductive groups, Comment. Math. Univ. St. Paul. 42 (1993), no. 2, 189-207. | MR | Zbl

,[16] Characteristic cycles and wave front cycles of representations of reductive groups, to appear in Annals of Math. | MR | Zbl | EuDML

and ,[17] Generalized Whittaker models for unitarizable highest weight representations (in Japanese), Master Thesis, Kyoto University, 1998.

,[18] Singular unitary representations, in Non commutative harmonic analysis and Lie groups, LNM 880 (1981), pp. 506 - 535. | MR | Zbl | DOI

,[19] Associated varieties and unipotent representations, in Harmonic analysis on reductive groups (Brunswick, ME, 1989), 315-388, Progr. Math. 101, Birkhäuser, Boston, Boston, MA, 1991. | MR | Zbl | DOI

, Jr.,[20] The method of coadjoint orbits for real reductive groups, in Representation Theory of Lie Groups (eds. J. Adams and D. Vogan), 177-238, IAS/Park City Mathematics Series 8, AMS, 2000. | MR | Zbl | DOI

, Jr.,[1] The local structure of characters, J. Funct. Anal. 37 (1980), no. 1, 27-55. | MR | Zbl | DOI

and , Jr.,[2] Differential operators on homogeneous spaces. I. Irreducibility of the associated variety for annihilators of induced modules, Invent. Math. 69 (1982), no. 3, 437-476. | MR | Zbl | EuDML | DOI

and ,[3] Differential operators on homogeneous spaces. III. Characteristic varieties of Harish-Chandra modules and of primitive ideals, Invent. Math. 80 (1985), no. 1, 1-68. | MR | Zbl | EuDML | DOI

and ,[4] Minimal representations of ${E}_{6},{E}_{7}$ and ${E}_{8}$ and the generalized Capelli identity, Proc. Nat. Acad. Sci. U.S.A. 91 (1994), no. 7, 2469-2472. | MR | Zbl | DOI

and ,[5] Minimal representations, geometric quantization, and unitarity, Proc. Nat. Acad. Sci. U.S.A. 91 (1994), no. 13, 6026-6029. | MR | Zbl | DOI

and ,[6] Lagrangian models of minimal representations of ${E}_{6},{E}_{7}$ and ${E}_{8}$, in Functional analysis on the eve of the 21st century, Vol. 1 (New Brunswick, NJ, 1993), 13-63, Progr. Math., 131, Birkhäuser, Boston, Boston, MA, 1995. | MR | Zbl

and ,[7] Characteristic cycles of holomorphic discrete series, Trans. Amer. Math. Soc. 334 (1992), no. 1, 213-227. | MR | Zbl | DOI

,[8] Characteristic cycles of discrete series for $\mathbb{R}$-rank one groups, Trans. Amer. Math. Soc. 341 (1994), 603-622. | MR | Zbl

,[9] Differential operators and highest weight representations, Mem. Amer. Math. Soc. 94 (1991), no. 455, iv+102 pp. | MR | Zbl

, and ,[10] Commutative Algebra with a View Toward Algebraic Geometry, GTM 150, Springer, New York, 1995. | MR | Zbl

,[11] A classification of unitary highest weight modules, in Representation theory of reductive groups (Park City, Utah, 1982), 97-143, Progr. Math., 40, Birkhäuser, Boston, Boston, Mass., 1983. | MR | Zbl | DOI

, and ,[12] Intersection theory, Springer, Berlin, 1984. | MR | Zbl | DOI

,[13] Young tableaux, With applications to representation theory and geometry. Cambridge Univ. Press, Cambridge, 1997. | MR | Zbl

,[14] Holomorphic discrete series for the real symplectic group, Invent. Math. 19 (1973), 49-58. | MR | Zbl | EuDML | DOI

,[15] Sulle varietà rappresentate coll'annulare determinanti minori contenuti in un determinante simmetrico generico di forme, Atti R. Accad. Sci. Torino 41 (1906), 102 - 125. | JFM

,[16] Algebraic geometry, A first course. Corrected reprint of the 1992 original, Springer, New York, 1995. | MR

,[17] On symmetric and skew-symmetric determinantal varieties, Topology 23 (1984), no. 1, 71-84. | MR | Zbl | DOI

and ,[18] Whittaker functions of generalized principal series on $SU(2,2)$, J. Math. Kyoto Univ. 37 (1997), no. 3, 531-546. | MR | Zbl | DOI

,[19] An explicit integral representation of Whittaker functions for the representations of the discrete series -the case of $SU(2,2)$, J. Math. Kyoto Univ. 37 (1997), no. 3, 519-530. | MR | Zbl | DOI

and ,[20] Differential geometry, Lie groups, and symmetric spaces, Academic Press, New York, 1978. | MR | Zbl

,[21] Rings and Fields, I., Iwanami Lecture Series, The Foundation of Modern Mathematics 15, Iwanami Shoten 1997.

,[22] Reciprocity laws in the theory of dual pairs, in Representation theory of reductive groups (Park City, Utah, 1982), 159-175, Progr. Math., 40, Birkhäuser, Boston, Boston, Mass., 1983. | MR | Zbl | DOI

,[23] Perspectives on invariant theory : Schur duality, multiplicity-free actions and beyond, in The Schur lectures (1992) (Tel Aviv), 1-182, Bar-Han Univ., Ramat Gan, 1995. | MR | Zbl

,[24] Remarks on classical invariant theory, Trans. Amer. Math. Soc. 313 (1989), no. 2, 539-570. | MR | Zbl | DOI

,Remarks on classical invariant theory", Trans. Amer. Math. Soc. 318 (1990), no. 2, 823. | MR | Zbl

, Erratum to : "[25] Dual pairs in physics : harmonic oscillators, photons, electrons, and singletons, in Applications of group theory in physics and mathematical physics (Chicago, 1982), 179-207, Amer. Math. Soc, Providence, R.I., 1985. | MR | Zbl

,[26] The Capelli identity, the double commutant theorem, and multiplicity-free actions, Math. Ann. 290 (1991), no. 3, 565-619. | MR | Zbl | EuDML | DOI

and ,[27] The minimal orbit in a simple Lie algebra and its associated maximal ideal, Ann. Sci. Ecole Norm. Sup. (4) 9 (1976), no. 1, 1-29. | MR | Zbl | EuDML | Numdam | DOI

,[28] On the Segal-Shale-Weil representations and harmonic polynomials, Invent. Math. 44 (1978), no. 1, 1-47. | MR | Zbl | EuDML | DOI

and ,[29] Characters of unitary representations of Lie groups, Funkcional. Anal, i Priložen 2 (1968), no. 2 40-55. | MR | Zbl

,[30] On Whittaker vectors and representation theory, Invent. Math. 48 (1978), no. 2, 101-184. | MR | Zbl | EuDML | DOI

,[31] Orbits and representations associated with symmetric spaces, Amer. J. Math. 93 (1971), 753-809. | MR | Zbl | DOI

and ,[32] Generalized Whittaker vectors and representation theory, Thesis, M.I.T., 1979. | MR

,[33] Commutative ring theory, Translated from the Japanese by M. Reid, Cambridge Univ. Press, Cambridge, 1986. | MR | Zbl

,[34] Whittaker vectors and associated varieties, Invent. math. 89 (1987), 219 - 224. | MR | Zbl | EuDML | DOI

,[35] ${C}^{-\infty}$-Whittaker vectors for complex semisimple Lie groups, wave front sets, and Goldie rank polynomial representations, Ann. Sci. Ecole Norm. Sup. (4) 23 (1990), no. 2, 311-367. | MR | Zbl | EuDML | Numdam | DOI

,[36] Whittaker vectors and the Goodman-Wallach operators, Acta Math. 161 (1988), no. 3-4, 183-241. | MR | Zbl | DOI

,[37] Bernstein degree of singular unitary highest weight representations of the metaplectic group. Proc. Japan Acad., 75, Ser. A (1999), 9 - 11. | MR | Zbl | DOI

and ,[38] An explicit integral representation of Whittaker functions on $Sp(2;\mathbf{R})$ for the large discrete series representations, Tôhoku Math. J. (2) 46 (1994), no. 2, 261-279. | MR | Zbl | DOI

,[39] Invariant theory. in Algebraic geometry. IV, A translation of Algebraic geometry. 4 (Russian), Akad. Nauk SSSR Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, Translation edited by A. N. Parshin and I. R. Shafarevich, Encyclopaedia of Mathematical Sciences, 55. Springer, Berlin, 1994. | Zbl | MR | DOI

and ,[40] Weil representation. I. Intertwining distributions and discrete spectrum, Mem. Amer. Math. Soc. 25 (1980), no. 231, iii+203 pp. | MR | Zbl

and ,[41] Kirillov's character formula for reductive Lie groups, Invent. Math. 48 (1978), no. 3, 207-220. | MR | Zbl | EuDML | DOI

,[42] On the stability of branching coefficients of rational representations of reductive groups, Comment. Math. Univ. St. Paul. 42 (1993), no. 2, 189-207. | MR | Zbl

,[43] On the characters of the discrete series. The Hermitian symmetric case, Invent. Math. 30 (1975), no. 1, 47-144. | MR | Zbl | EuDML | DOI

,[44] Characteristic cycles and wave front cycles of representations of reductive groups, to appear in Annals of Math. | MR | Zbl | EuDML

and ,[45] Invariant theory, Lecture Notes in Mathematics, Vol. 585. Lecture Notes in Math., 585, Springer, Berlin, 1977. | MR | Zbl

,[46] Discrete series Whittaker functions of $SU(n,1)$ and $\mathrm{Spin}(2n,1)$, J. Math. Sci. Univ. Tokyo 3 (1996), no. 2, 331-377. | MR | Zbl

,[47] Sur le caractère de la représentation de Shale-Weil de $\mathrm{Mp}(n,\mathbf{R})$ et $\mathrm{Sp}(n,\mathbf{C})$, Math. Ann. 252 (1980), no. 1, 53-86. | MR | Zbl | EuDML | DOI

,[48] On a class of quasihomogeneous affine varieties. Math. USSR Izvestja, 6 (1972), 743 - 758. | Zbl | DOI

and ,[49] Gel'fand-Kirillov dimension for Harish-Chandra modules, Invent. Math. 48 (1978), no. 1, 75-98. | MR | Zbl | EuDML | DOI

, Jr.,[50] Singular unitary representations. In Non commutative harmonic analysis and Lie groups, LNM 880 (1981), pp. 506 - 535. | MR | Zbl | DOI

,[51] Associated varieties and unipotent representations, in Harmonic analysis on reductive groups (Brunswick, ME, 1989), 315-388, Progr. Math. 101, Birkhäuser, Boston, Boston, MA, 1991. | MR | Zbl | DOI

, Jr.,[52] The Method of Coadjoint Orbits for Real Reductive Groups, in Representation Theory of Lie Groups, 177-238, IAS/Park City math. ser. 8, Amer. Math. Soc, (2000). | MR | Zbl | DOI

, Jr.,[53] Embeddings of discrete series into induced representations of semisimple Lie groups. II. Generalized Whittaker models for $SU(2,2)$, J. Math. Kyoto Univ. 31 (1991), no. 2, 543-571. | MR | Zbl | DOI

,[54] private communication (1999). (See Yamashita's article in this volume.)

,[1] Szegö kernels associated with Zuckerman modules, J. Funct. Anal., 131 (1995), 145-182. | MR | Zbl | DOI

,[2] Covariant differential operators, Math. Ann., 288 (1990), 731-739. | MR | Zbl | EuDML | DOI

, and ,[3] Differential operators and highest weight representations, Mem. Amer. Math. Soc. No. 455, American Mathematical Society, Providence, R.I., 1991. | MR | Zbl

, and ,[4] Szegö maps and highest weight representations, Pacific J. Math., 158 (1993), 67-91. | MR | Zbl | DOI

and ,[5] An intrinsic analysis of unitarizable highest weight modules, Math. Ann., 288 (1990), 571-594. | MR | Zbl | EuDML | DOI

and ,[6] A proof of a conjecture of Kashiwaxa and Vergne. in "Noncommutative harmonic analysis and Lie groups (Marseille, 1980)", Lecture Notes in Math., 880, Springer, Berlin-New York, 1981, pp. 74-90. | MR | Zbl | DOI

and ,[7] A classification of unitary highest weight modules, in "Representation theory of reductive groups (Park City, Utah, 1982 ; P.C.Trombi ed.)", Progress in Math., Vol. 40, Birkhäuser, 1983, pp.97-143. | MR | Zbl

, , and ,[8] Associated variety, Kostant-Sekiguchi correspondence, and locally free $U\phantom{\rule{0.166667em}{0ex}}\left(n\right)$-action on Harish-Chandra modules, J. Math. Soc. Japan, 51 (1999), 129-149. | MR | Zbl | DOI

and ,[9] Singular holomorphic representations and singular modular forms, Math. Ann., 259 (1982), 227-244. | MR | Zbl | EuDML | DOI

and ,[10] Multiplicity formulae for discrete series, Invent. Math., 26 (1974), 133-178. | MR | Zbl | EuDML | DOI

and ,[11] Quasi-equivariant $\mathcal{D}$-modules, equivariant derived category, and representations of reductive Lie groups, in "Lie theory and geometry (J.L.Brylinski et al. eds.)", Birkhäuser, 1994, pp.457-488. | MR | Zbl

and ,[12] On the Segal-Shale-Weil representations and harmonic polynomials, Invent. Math., 44 (1978), 1-47. | MR | Zbl | EuDML | DOI

and ,[13] The degrees of orbits of the multiplicity actions, in this volume. | Zbl

and ,[14] Generalized Gelfand-Graev representation and Ennola duality, in "Algebraic groups and related topics", Advanced Studies in Pure Math., 6 (1985), 175-206. | MR | Zbl | DOI

,[15] Generalized Gelfand-Graev representations of exceptional simple algebraic groups over a finite field. I, Invent. Math., 84 (1986), 575-616. | MR | Zbl | EuDML | DOI

,[16] Lie groups beyond an introduction. Progress in Mathematics Vol. 140, Birkhäuser, Boston-Besel-Stuttgart, 1996. | MR | Zbl

,[17] Lie group representations on polynomial rings, Amer. J. Math., 85 (1963), 327-404. | MR | Zbl | DOI

,[18] On Whittaker vectors and representation theory, Invent. Math., 48 (1978), 101-184. | MR | Zbl | EuDML | DOI

,[19] Young diagrammatic methods for the restriction of representations of complex classical Lie groups to reductive subgroups of maximal rank, Adv. Math., 79 (1990), 104-135. | MR | Zbl | DOI

and ,[20] An intrinsic classification of the unitarizable highest weight modules as well as their associated varieties, Compositio Math. 101 (1996), 313-352. | MR | Zbl | EuDML | Numdam

,[21] Annihilators and associated varieties of unitary highest weight modules, Ann. Sci. Éc. Norm. Sup., 25 (1992), 1-45. | MR | Zbl | EuDML | Numdam | DOI

,[22] Whittaker vectors and associated varieties, Invent. Math., 89 (1987), 219-224. | MR | Zbl | EuDML | DOI

,[23] Whittaker vectors and the Goodman-Wallach operators, Acta Math., 161 (1988), 183-241. | MR | Zbl | DOI

,[24] ${C}^{-\infty}$-Whittaker vectors for complex semisimple Lie groups, wave front sets, and Goldie rank polynomial representations, Ann. Sci. Éc. Norm. Sup., 23 (1990), 311-367. | MR | Zbl | EuDML | Numdam | DOI

,[25] ${C}^{-\infty}$-Whittaker vectors corresponding to a principal nilpotent orbit of a real reductive linear Lie group, and wave front sets. Compositio Math. 82 (1992), 189-244. | MR | Zbl | EuDML | Numdam

,[26] Modèles de Whittaker dégénérés pour des groupes $p$-adiques, Math. Z. 196 (1987), 427-452. | MR | Zbl | EuDML | DOI

and ,[27] Bernstein degree and associated cycles of Harish-Chandra modules - Hermitian symmetric case, in this volume. | Zbl

, and ,[28] Homogeneous complex manifolds and representations of semisimple Lie groups, Dissertation, University of California, Berkeley, 1967 ; reprinted in "Representation theory and harmonic analysis on semisimple Lie groups (P.L Sally and D.A Vogan eds.)", Mathematical Surveys and Monograph Vol. 31, Amer. Math. Soc, 1989, pp.223- 286. | MR | Zbl

,[29] Boundary value problems for group invariant differential equations, in "Elie Cartan et les Mathématiques d'Aujourd'hui", Astérisque, Numéro hors-série, 1985, pp.311-321. | MR | Numdam | Zbl

,[30] The explicit Fourier decomposition of ${L}^{2}(SO\left(n\right)/SO(n-m))$, Canad. J. Math., 27 (1975), 294-310. | MR | Zbl

,[31] Generalized Whittaker models for unitarizable highest weight representations (in Japanese), Master Thesis, Kyoto University, 1998.

,[32] Analytic continuation of the holomorphic discrete series of a semi-simple Lie group, Acta Math., 136 (1976), 1-59. | MR | Zbl | DOI

and ,[33] Associated varieties and unipotent representations, in "Harmonic Analysis on Reductive Groups (W.Barker and P.Sally eds.)," Progress in Math., Vol. 101, Birkhäuser, 1991, pp.315-388. | MR | Zbl | DOI

,[34] The analytic continuation of the discrete series. II, Trans. Amer. Math. Soc, 251 (1979), 19-37. | MR | Zbl | DOI

,[35] Real reductive groups I, Pure and Applied Mathematics Vol. 132, Academic Press, San Diego-London, 1988. | MR | Zbl

,[36] Harmonic analysis on semi-simple Lie groups I, Springer-Verlag, Berlin-Heidelberg-New York, 1972. | MR | Zbl

,[37] The classical groups. Their invariants and representations, Eighth printing, Princeton University Press, Princeton, NJ, 1973. | Zbl

,[38] Dolbeault cohomological realization of Zuckerman modules associated with finite rank representations, J. Funct. Anal., 129 (1995), 428-454. | MR | Zbl | DOI

,[39] On Whittaker vectors for generalized Gelfand-Graev representations of semisimple Lie groups, J. Math. Kyoto Univ., 26 (1986), 263-298. | MR | Zbl | DOI

,[40] Finite multiplicity theorems for induced representations of semisimple Lie groups II : Applications to generalized Gelfand-Graev representations, J. Math. Kyoto. Univ., 28 (1988), 383-444. | MR | Zbl | DOI

,[41] Multiplicity one theorems for generalized Gelfand-Graev representations of semisimple Lie groups and Whittaker models for the discrete series, Advanced Studies in Pure Math. 14 (1988), 31-121. | MR | Zbl | DOI

,[42] Embeddings of discrete series into induced representations of semisimple Lie groups I,: General theory and the case of $SU(2,2)$, Japan. J. Math., 16 (1990), 31-95; | MR | Zbl | DOI

,Embeddings of discrete series into induced representations of semisimple Lie groups II : generalized Whittaker models for $SU(2,2)$, J. Math. Kyoto Univ., 31 (1991), 543-571. | MR | Zbl | DOI

,[43] Criteria for the finiteness of restriction of $U\left(\U0001d524\right)$-modules to subalgebras and applications to Harish-Chandra modules: a study in relation to the associated varieties, J. Funct. Anal., 121 (1994), 296-329. | MR | Zbl | DOI

,[44] Description of the associated varieties for the discrete series representations of a semisimple Lie group: An elementary proof by means of differential operators of gradient type, Comment. Math. Univ. St. Paul., 47 (1998), 35-52. | MR | Zbl

,[45] The embeddings of discrete series into principal series for an exceptional real simple Lie group of type ${G}_{2}$, J. Math. Kyoto Univ., 36 (1996), 557-595. | MR | Zbl | DOI

and ,[1] A classification of unitary highest weight modules, Progress in Math. 40 (1983) 97-143, Birkhäuser. | MR | Zbl

, and ,[2] An intrinsic analysis of unitarizable highest weight modules, Math. Ann. 288 (1990) 571-594. | MR | Zbl | EuDML | DOI

and ,[3] Analysis on symmetric cones, Oxford, 1994. | MR | Zbl

and ,[4] Intersection theory, Springer, Berlin, 1984. | MR | Zbl | DOI

,[5] Differential geometry, Lie groups, and symmetric spaces Academic Press, New York, San Francisco, London. (1978). | MR | Zbl

,[6] The Capelli identity, the double commutant theorem, and multiplicity-free actions, Math. Ann. 290 (1991) 565-619. | MR | Zbl | EuDML | DOI

and ,[7] Hermitian symmetric spaces and their unitary highest weight modules, Jour. Funct. Anal. 52 (1983) 385-412. | MR | Zbl | DOI

,[8] On a ring of invariant polynomials on a hermitian symmetric space, J. Algebra, 67 (1980) 72-81. | MR | Zbl | DOI

,[9] Annihilators and associated varieties of unitary highest weight modules, Ann. scient. École Normal Superior, (1992) 1-45. | MR | Zbl | EuDML | Numdam

,[10] Some remarks on nilpotent orbits, J. Algebra 64 (1980) 190-213. | MR | Zbl | DOI

,[11] The Selberg-Jack symmetric functions, Adv. Math. 130 (1997) 33-102. | MR | Zbl | DOI

,[12] The Gelfand-Kirillov dimension and Bernstein degree of a unitary highest weight module, Master thesis, Kyushu University (2000) in Japanese.

,[13] Representation Theory of Semisimple Groups, An Overview Based on Examples, Princeton Univ. Press, 1986 | MR | Zbl | DOI

,[14] Orbits and representations associated with symmetric spaces, Amer. J. Math., 93 (1971) 753-809. | MR | Zbl | DOI

and ,[15] The correspondences of infinitesimal characters for reductive dual pairs in semisimple Lie groups, Duke Math. J. 97 (1999) 347-377. | MR | Zbl | DOI

,[16] Symmetric functions and Hall polynomials, 2nd ed., Oxford, 1995 | MR | Zbl

,[17] Compactification of symmetric spaces, II, Amer. J. Math. 86 (1964), 358-378. | MR | Zbl | DOI

,[18] Bernstein degree of singular unitary highest weight representations of the metaplectic group, Proc. Japan Acad. Ser. A, 75 (1999) 9-11. | MR | Zbl | DOI

and ,[19] Bernstein degree and associated cycles of Harish-Chandra modules - Hermitian symmetric case -, in this volume. | Zbl

, and ,[20] Les paires duales dans les algèbres de Lie r'eductives, Astérisque 219 (1994), 1-121. | MR | Zbl

,[21] Die Randwerte holomorpher Funktionen auf hermitesch symmetrischen Räumen, Invent. Math. 9 (1969/1970) 61-80. | MR | Zbl | EuDML | DOI

,[22] Associated varieties and unipotent representations, Progress in Math. 101 (1991) 315-388. | MR | Zbl

,[23] The analytic continuation of the discrete series, I, II, Trans. Amer. Math. Soc. 251 (1979) 1-17, 19-37. | MR | Zbl

,[24] Cayley transform and generalized Whittaker models for irreducible highest weight modules, in this volume. | Zbl

,[Intro] Introduction to this volume.

[NOT] Bernstein degree and associated cycles of Harish-Chandra modules - Hermitian symmetric case -. In this volume. | Zbl

, and ,[Y] Cayley transform and generalized Whittaker models for irreducible highest weight modules. In this volume. | Zbl

,[1] A theory of Stiefel harmonics. Trans. AMS 192 (1974), 29 - 50. | MR | Zbl | DOI

,[2] Associated variety, Kostant-Sekiguchi correspondence, and locally free $U\left(n\right)$-action on Harish-Chandra modules. J. Math. Soc. Japan 51 (1999), no. 1, 129-149. | MR | Zbl | DOI

and ,[3] Singular unitary representations of classical groups. Invent. Math. 97 (1989), no. 2, 237-255. | MR | Zbl | EuDML | DOI

,[4] ${C}^{-\infty}$-Whittaker vectors corresponding to a principal nilpotent orbit of a real reductive linear Lie group, and wave front sets. Compositio Math. 82 (1992), 189-244. | MR | Zbl | EuDML | Numdam

,[5] On the stability of branching coefficients of rational representations of reductive groups, Comment. Math. Univ. St. Paul. 42 (1993), no. 2, 189-207. | MR | Zbl

,[6] Characteristic cycles and wave front cycles of representations of reductive groups. To appear in Annals of Math. | MR | Zbl | EuDML

and ,[7] Annihilators, associated varieties, and the theta correspondence, preprint, November 1999.

,