no. 2
C -∞ -Whittaker vectors corresponding to a principal nilpotent orbit of a real reductive linear Lie group, and wave front sets
Compositio Mathematica, Tome 82 (1992) no. 2, pp. 189-244. 
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     author = {Matumoto, Hisayosi},
     title = {$C^{-\infty }${-Whittaker} vectors corresponding to a principal nilpotent orbit of a real reductive linear {Lie} group, and wave front sets},
     journal = {Compositio Mathematica},
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     publisher = {Kluwer Academic Publishers},
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     year = {1992},
     zbl = {0797.22005},
     language = {en},
     url = {http://archive.numdam.org/item/CM_1992__82_2_189_0/}
}
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Matumoto, Hisayosi. $C^{-\infty }$-Whittaker vectors corresponding to a principal nilpotent orbit of a real reductive linear Lie group, and wave front sets. Compositio Mathematica, Tome 82 (1992) no. 2, pp. 189-244. http://archive.numdam.org/item/CM_1992__82_2_189_0/

[1] D. Barbasch and D.A. Vogan Jr.: The local structure of characters, J. Funct. Anal. 37 (1980), 27-55. | MR | Zbl

[2] D. Barbasch and D.A. Vogan Jr.: Primitive ideals and orbital integrals in complex classical groups, Math. Ann. 259 (1982), 153-199. | MR | Zbl

[3] D. Barbasch and D.A. Vogan Jr.: Primitive ideals and orbital integrals in complex exceptional groups, J. Algebra 80 (1983), 350-382. | MR | Zbl

[4] D. Barbasch and D.A. Vogan Jr.: Unipotent representations of complex semisimple Lie groups, Ann. of Math. 121 (1985), 41-110. | MR | Zbl

[5] D. Barbasch and D.A. Vogan Jr.: Weyl group representations and nilpotent orbits, in: P.C. Trombi (ed.), Representation Theory of Reductive Groups, Progress in Mathematics Vol. 40, 21-33, Birkhäuser, Boston-Basel- Stuttgart, 1983. | MR | Zbl

[6] J. Bernstein and S.I. Gelfand: Tensor product of finite and infinite dimensional representations of semisimple Lie algebras, Compositio Math. 41 (1980), 245-285. | Numdam | MR | Zbl

[7] D. Bump: Automorphic Forms on GL(3, R), Lecture Notes in Mathematics No. 1083, Springer-Verlag, Berlin-Heidelberg-New York, 1984. | MR | Zbl

[8] W. Casselman: A letter to Harish-Chandra, November 30, 1982.

[9] W. Casselman: Canonical extensions of Harish-Chandra modules to representations of G, Can. J. Math. 41 (1989), 385-438. | MR | Zbl

[10] L.G. Casian: Primitive ideals and representations, J. of Algebra 101 (1986), 497-515. | MR | Zbl

[11] R. Goodman: Horospherical functions on symmetric spaces, Canadian Mathematical Society Conference Proceedings 1 (1981), 125-133. | Zbl

[12] R. Goodman and N.R. Wallach: Whittaker vectors and conical vectors, J. Funct. Anal. 39 (1980), 199-279. | MR | Zbl

[13] M. Hashizume: Whittaker models for semisimple Lie groups, Japan J. Math. 5 (1979), 349-401. | MR | Zbl

[14] M. Hashizume: Whittaker functions on semisimple Lie groups, Hiroshima Math. J. 13 (1982), 259-293. | MR | Zbl

[15] H. Hecht and W. Schmid: A proof of Blattner's conjecture, Invent. Math. 31 (1975), 129-154. | MR | Zbl

[16] L. Hörmander: Fourier integral operators I, Acta Math. 127 (1971), 79-183. | MR | Zbl

[17] R. Howe: Wave front sets of representations of Lie groups, in: Automorphic Forms, Representation Theory, and Arithmetic, Bombay, 1981. | MR | Zbl

[18] H. Jacquet: Fonction de Whittaker associées aux groupes de Chevalley, Bull. Soc. Math. France 95 (1967), 243-309. | Numdam | MR | Zbl

[19] H. Jacquet and R.P. Langlands: Automorphic Form on GL(2), Lecture Notes in Mathematics, No. 114, Springer-Verlag, Berlin-Heidelberg-New York, 1970. | MR | Zbl

[20] A. Joseph: Goldie rank in the enveloping algebra of a semisimple Lie algebra I, J. Algebra 65 (1980), 269-283. | MR | Zbl

[21] A. Joseph: Goldie rank in the enveloping algebra of a semisimple Lie algebra II, J. Algebra 65 (1980), 284-306. | MR | Zbl

[22] A. Joseph: On the associated variety of a primitive ideal, J. Algebra 93 (1985), 509-523. | MR | Zbl

[23] M. Kashiwara: The invariant holonomic system on a semisimple Lie group, in: Algebraic Analysis (papers dedicated to Professor Mikio Sato on the occasion of his sixtieth birthday) Vol. 1, pp. 277-286, Academic Press, San Diego, 1988. | MR | Zbl

[24] M. Kashiwara and T. Kawai: Second-microlocalization and asymptotic expansions, in: Lecture Notes in Physics No. 126, pp. 21-76, Springer-Verlag, Berlin-Heidelberg -New York, 1980. | MR | Zbl

[25] M. Kashiwara and M. Vergne: Functions on the Shilov boundary of the generalized half plane, in: Non-Commutative Harmonic Analysis, Lecture Notes in Mathematics No. 728, Springer-Verlag, Berlin-Heidelberg- New York, 1979. | MR | Zbl

[26] M. Kashiwara and M. Vergne: K-types and the singular spectrum, in: Non-Commutative Harmonic Analysis, Lecture Notes in Mathematics No. 728, Springer-Verlag, Berlin-Heidelberg-New York, 1979. | MR | Zbl

[27] N. Kawanaka: Shintani lifting and generalized Gelfand-Graev representations, Proc. Symp. Pure Math. 47 (1987), 147-163. | MR | Zbl

[28] D.R. King: The primitive ideals associated to Harish-Chandra modules and certain harmonic polynomials, Thesis, M.I.T., 1979.

[29] D.R. King: The character polynomial of the annihilator of an irreducible Harish-Chandra module, Amer. J. Math. 103 (1981), 1195-1240. | MR | Zbl

[30] A.W. Knapp: Commutativity of intertwining operators for semisimple groups, Compo. Math. 46 (1982), 33-84. | Numdam | MR | Zbl

[31] A.W. Knapp: Representation Theory of Semisimple Groups, An Overview Based on Examples, Princeton Mathematical series 36, Princeton University Press, Lawrenceville, New Jersey, 1986. | MR | Zbl

[32] A.W. Knapp and G.J. Zuckerman: Classification theorems for representations of semisimple groups, in: Non-Commutative Harmonic Analysis, Lecture Notes in Mathematics, Vol. 587 (1977), 138-159. | MR | Zbl

[33] A.W. Knapp and G.J. Zuckerman: Classification of irreducible tempered representations of semisimple groups, Ann. of Math. 116 (1982), 389-501. | MR | Zbl

[34] B. Kostant: The principal three dimensional subgroup and the Betti numbers of a complex simple Lie group, Amer. J. of Math. 81 (1959), 973-1032. | MR | Zbl

[35] B. Kostant: Lie group representations on polynomial rings, Amer. J. of Math. 86 (1963), 327-402. | MR | Zbl

[36] B. Kostant: On Whittaker vectors and representation theory, Invent. Math. 48 (1978), 101-184. | MR | Zbl

[37] B. Kostant and S. Rallis: Orbits and representations associated with symmetric spaces, Amer. J. of Math. 93 (1971), 753-809. | MR | Zbl

[38] J. Lepowski and N.R. Wallach: Finite- and infinite-dimensional representations of linear semisimple groups, Trans. Amer. Math. Soc. 184 (1973), 223-246. | MR | Zbl

[39] G. Lusztig and J.N. Spaltenstein: Induced unipotent classes, J. London Math. Soc. 19 (1979), 41-52. | MR | Zbl

[40] T.E. Lynch: Generalized Whittaker vectors and representation theory, Thesis, M.I.T., 1979.

[41] I.G. Macdonald:Some irreducible representations of Weyl groups, Bull. London Math. Soc. 4 (1972), 148-150. | MR | Zbl

[42] Hideya Matsumoto: Quelques remarques sur les groupes de Lie algébriques réels, J. Math. Soc. Japan 16 (1964), 419-446. | MR | Zbl

[43] Hisayosi Matumoto: Boundary value problems for Whittaker functions on real split semisimple Lie groups, Duke Math. J. 53 (1986), 635-676. | MR | Zbl

[44] H. Matumoto: Whittaker vectors and associated varieties, Invent. Math. 89 (1987), 219-224. | MR | Zbl

[45] H. Matumoto: Cohomological Hardy space for SU(2, 2): Adv. Stud. in Pure Math. Vol. 14, Kinokuniya Book Store and North-Holland, 1986. | Zbl

[46] H. Matumoto: Whittaker vectors and the Goodman-Wallach operators: Acta Math. 161 (1988), 183-241. | MR | Zbl

[47] H. Matumoto: Whittaker modules associated with highest weight modules, Duke Math. J. 60 (1989), 59-113. Erratum, ibid. 61 (1990), 973. | MR | Zbl

[48] H. Matumoto: C-∞-Whittaker vectors for complex semisimple Lie groups, wave front sets, and Goldie rank polynomial representations, Ann. Scient. Ec. Norm. Sup. 23 (1990), 311-367. Erratum, ibid. 23 (1990), 668. | Numdam | Zbl

[49] C Mœglin and J.L. Waldspurger: Modèles de Whittaker dénérés pour des groupes p-adiques, Math. Z. 196 (1987), 427-452. | Zbl

[50] K. Nishiyama: Virtual character modules of semisimple Lie groups and representations of Weyl groups, J. Math. Soc. Japan 37, 719-740. | MR | Zbl

[51] R. Rao: Orbital integrals in reductive Lie groups, Ann. of Math. 96 (1972), 505-510. | MR | Zbl

[52] F. Rodier: Modèle de Whittaker et caractères de representations, in: Non-Commutative Harmonic Analysis, Lecture Notes in Pure Mathematics No. 466, pp. 151-171, Springer-Verlag, Berlin-Heidelberg-New York, 1981. | MR | Zbl

[53] W. Rossman: Limit orbits in reductive Lie algebras, Duke Math. J. 49 (1982), 215-229. | MR | Zbl

[54] W. Rossman: Tempered representations and orbits, Duke Math. J. 49 (1982), 231-247. | MR | Zbl

[55] L.P. Rothschild: Orbits in a real reductive Lie algebra, Trans. Amer. Math. Soc. 168 (1972), 403-421. | MR | Zbl

[56] M. Sato, T. Kawai, and M. Kashiwara: Microfunctions and pseudo-differential equations, in: Hyperfunctions and Pseudo-Differential Equations, Lecture Notes in Mathematics No. 287, pp. 264-529, Springer-Verlag, Berlin-Heidelberg-New York, 1971. | MR | Zbl

[57] G. Schiffmann: Intégrales d'entrelacement et fonctions de Whittaker, Bull. Soc. Math. France 99 (1971), 3-72. | Numdam | MR | Zbl

[58] W. Schmid: On the characters of the discrete series (the Hermitian symmetric case), Invent. Math. 30 (1975), 47-144. | MR | Zbl

[59] W. Schmid: Two character identities for semisimple Lie groups, in: Non-Commutative Harmonic Analysis, Springer Lecture Notes in Math. Vol. 587, 1977, pp. 196-225. | MR | Zbl

[60] W. Schmid: Boundary value problems for group invariant differential equations, in: Proceedings of the Cartan Symposium, Lyon, 1984, Asterisque. | Numdam | MR | Zbl

[61] J. Sekiguchi: The nilpotent subvariety of the vector space associated to a symmetric pair, Publ. RIMS. Kyoto Univ. 20 (1984), 155-212. | MR | Zbl

[62] F. Shahidi: Whittaker models for real groups, Duke Math. J. 47 (1980), 99-125. | MR | Zbl

[63] G. Shalika: The multiplicity one theorem for GL(n), Ann. of Math. 100 (1974), 171-193. | MR | Zbl

[64] B. Speh and D.A. Vogan Jr.: Reducibility of generalized principal series representations, Acta. Math. 145 (1980), 227-299. | MR | Zbl

[65] F. Treves: Introduction to Pseudodifferential and Fourier Integral Operators, Volume 1, Pseudodifferential Operators, Plenum Press, New York and London, 1980. | MR | Zbl

[66] D.A. Vogan Jr.: Gelfand-Kirillov dimensions for Harish-Chandra modules, Invent. Math. 48 (1978), 75-98. | MR | Zbl

[67] D.A. Vogan Jr.: Representations of Real Reductive Lie Groups, Progress in Mathematics, Birkhäuser, 1982. | Zbl

[68] D.A. Vogan Jr.: The orbit method and primitive ideals for semisimple Lie algebras, Canadian Mathematical Society Conference Proceedings Vol. 5 Lie Algebras and Related Topics (1986), 281-316. | MR | Zbl

[69] D.A. Vogan Jr.: Irreducible characters of semisimple Lie groups IV, character-multiplicity duality, Duke Math. J. 49 (1982), 943-1073. | MR | Zbl

[70] D.A. Vogan Jr.: Unitarizability of certain series of representations, Ann. of Math. 120 (1984), 141-187. | MR | Zbl

[71] D.A. Vogan Jr.: Representations of reductive Lie groups, in: Proceedings of the International Congress of Mathematics, Berkeley, California, USA, 1986. | Zbl

[72] N.R. Wallach: Asymptotic expansions of generalized matrix entries of representations of real reductive groups, in: Lie group representations I, Lecture Notes in Pure Mathematics No. 1024, pp. 287-369, Springer-Verlag, Berlin-Heidelberg-New York, 1983. | MR | Zbl

[73] N.R. Wallach: Real Reductive Groups I, Academic Press, 1987. | MR | Zbl

[74] N.R. Wallach: Lie algebra cohomology and holomorphic continuation of generalized Jacquet integrals, Adv. Stud. in Pure Math. Vol. 14, pp. 123-151, Kinokuniya Book Store, 1986. | MR | Zbl

[75] G. Warner: Harmonic Analysis on Semi-Simple Lie Groups I, Die Drundlehren der mathematischen Wissenschaften in Einzeldarstellungen, Band 188, Springer-Verlag, Berlin-Heidelberg -New York, 1972. | MR | Zbl

[76] H. Yamashita: Multiplicity one theorems for generalized Gelfand-Graev representations of semisimple Lie groups and Whittaker models for the discrete series, Adv. Stud. in Pure Math. Vol. 14, pp. 31-121, Kinokuniya Book Store, 1986. | MR | Zbl

[77] G.J. Zuckerman: Tensor products of finite and infinite dimensional representations of semisimple Lie groups, Ann. of Math. 106 (1977), 295-308. | MR | Zbl