An intrinsic classification of the unitarizable highest weight modules as well as their associated varieties
Compositio Mathematica, Tome 101 (1996) no. 3, pp. 313-352. 
@article{CM_1996__101_3_313_0,
     author = {Jakobsen, Hans Plesner},
     title = {An intrinsic classification of the unitarizable highest weight modules as well as their associated varieties},
     journal = {Compositio Mathematica},
     pages = {313--352},
     publisher = {Kluwer Academic Publishers},
     volume = {101},
     number = {3},
     year = {1996},
     mrnumber = {1394518},
     zbl = {0861.22010},
     language = {en},
     url = {http://archive.numdam.org/item/CM_1996__101_3_313_0/}
}
TY  - JOUR
AU  - Jakobsen, Hans Plesner
TI  - An intrinsic classification of the unitarizable highest weight modules as well as their associated varieties
JO  - Compositio Mathematica
PY  - 1996
SP  - 313
EP  - 352
VL  - 101
IS  - 3
PB  - Kluwer Academic Publishers
UR  - http://archive.numdam.org/item/CM_1996__101_3_313_0/
LA  - en
ID  - CM_1996__101_3_313_0
ER  - 
%0 Journal Article
%A Jakobsen, Hans Plesner
%T An intrinsic classification of the unitarizable highest weight modules as well as their associated varieties
%J Compositio Mathematica
%D 1996
%P 313-352
%V 101
%N 3
%I Kluwer Academic Publishers
%U http://archive.numdam.org/item/CM_1996__101_3_313_0/
%G en
%F CM_1996__101_3_313_0
Jakobsen, Hans Plesner. An intrinsic classification of the unitarizable highest weight modules as well as their associated varieties. Compositio Mathematica, Tome 101 (1996) no. 3, pp. 313-352. http://archive.numdam.org/item/CM_1996__101_3_313_0/

1 Bernstein, I.N., Gelfand, I.M. and Gelfand, S.I.: Differential operators on the base affine space and a study of g-modules, in 'Lie Groups And Their Representations', Adam Hilger, London, 1975. | Zbl

2 Boe, B.: Homomorphisms between generalized Verma modules, Dissertation, Yale University, 1982. | Zbl

3 Boe, B. and Collingwood, D.: Intertwining operators between holomorphically induced modules, Pac. J. Math. 124 (1986), 73-84. | MR | Zbl

4 Boe, B. and Collingwood, D.: A multiplicity one theorem for holomorphically induced representations, Math. Z. 192 (1986), 265-282. | EuDML | MR | Zbl

5 Davidson, M.G. and Stanke, R.J.: Gradient-type differential operators and unitary highest weight representations of SU(p, q), J. Funct. Anal. 81 (1988), 100-125. | MR | Zbl

6 Davidson, M.G., Enright, T.J. and Stanke, R.J.: Differential operators and highest weight representations, Memoirs of the A.M.S. #455 (1991). | MR | Zbl

7 Deodhar, V.V.: Some characterizations of the Bruhat ordering on a Coxeter group and characterization of the relative Möbius function, Invent. Math. 39 (1977), 187-198. | EuDML | MR | Zbl

8 Enright, T.J., Howe, R. and Wallach, N.: A classification of unitary highest weight modules, in Representation Theory Of Reductive Groups, P.C. Trombi (eds.) (1983), 97-143. | MR | Zbl

9 Enright, T.J. and Joseph, A.: An intrinsic analysis of unitarizable highest weight modules, Preprint 1990. | MR | Zbl

10 Enright, T.J. and Parthasarathy, R.: A proof of a conjecture of Kashiwara and Vergne, in Non-commutative Harmonic Analysis, Marseille-Luminy 1980, Springer Lecture Notes in Mathematics, 880 (1981), 74-90. | MR | Zbl

11 Harish-Chandra, Representations of semi-simple Lie groups IV, V, VI., Amer. Jour. Math. 77 (1955), 743-777; 78 (1956), 1-41; 78 (1956), 564-628. | Zbl

12 Harris, M. and Jakobsen, H.P.: Covariant differential operators, in Group Theoretical Methods In Physics, Istanbul 1982, Springer Lecture Notes in Physics 180, 1983. | MR | Zbl

13 Jakobsen, H.P. and Vergne, M.: Wave and Dirac operators and representations of the conformal group, J. Funct. Anal. 24 (1977), 52-106. | MR | Zbl

14 Jakobsen, H.P. and Vergne, M.: Restrictions and expansions of holomorphic representations, J. Funct. Anal. 34 (1979), 29-53. | MR | Zbl

15 Jakobsen, H.P.: On singular holomorphic representations, Invent. Math. 62 (1980), 67-78. | EuDML | MR | Zbl

16 Jakobsen, H.P.: The last possible place of unitarity for certain highest weight modules, Math. Ann. 256 (1981), 439-447. | EuDML | MR | Zbl

17 Jakobsen, H.P.: Hermitian symmetric spaces and their unitary highest weight modules, J. Funct. Anal. 52 (1983), 385-412. | MR | Zbl

18 Jakobsen, H.P.: Basic covariant differential operators on hermitian symmetric spaces, Ann. scient. Èc. Norm. Sup. 18 (1985), 421-436. | EuDML | Numdam | MR | Zbl

19 James, G.D.: 'The Representation Theory of the Symmetric Groups', Springer Lecture Notes in Math. #682, Springer Verlag, Berlin-Heidelberg- New York 1978. | Zbl

20 Joseph, A.: Annihilators and associated varieties of unitary highest weight modules, Preprint 1990, To appear in Ann. scient. Èc. Norm. Sup. | EuDML | Numdam | MR | Zbl

21 Kashiwara, M. and Vergne, M.: On the Segal-Shale-Weil representation and harmonic polynomials, Invent. Math. 44 (1978), 1-47. | EuDML | MR | Zbl

22 Knapp, A. and Okamoto, K.: Limits of holomorphic discrete series, J. Funct. Anal. 9 (1972), 375-409. | MR | Zbl

23 Mack, G.: All unitary ray representations of the conformal group SU(2,2) with positive energy, Comm. Math. Phys. 55 (1977), 1-28. | MR | Zbl

24 Parthasarathy, K.R.: Criteria for the unitarizability of some highest weight modules, Proc. Indian Acad. Sci. 89 (1980), 1-24. | MR | Zbl

25 Rossi, H. and Vergne, M.: Analytic continuation of the holomorphic discrete series of a semi-simple Lie group, Acta Math. 136 (1976), 1-59. | MR | Zbl

26 Rühl, W.: Distributions on Minkowski space and their connection with analytic representations of the conformal group, Comm. Math. Phys. 27 (1972), 53-86. See also Ibid. 30 (1973), 287-302 and 34 (1973), 149-166. | MR | Zbl

27 Schmid, W.: Die Randwerte holomorpher Funktionen auf hermitesch symmetrischen Räumen, Invent. Math. 9 (1969), 61-80. | EuDML | MR | Zbl

28 Wallach, N.: Analytic continuation of the holomorphic discrete series II, Trans. Amer. Math, Soc. 260 (1980), 563-573. | MR | Zbl