@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}, volume = {104}, year = {1996}, pages = {313-352}, mrnumber = {1394518}, zbl = {0861.22010}, language = {en}, url = {http://dml.mathdoc.fr/item/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 104 (1996) pp. 313-352. http://gdmltest.u-ga.fr/item/CM_1996__101_3_313_0/
1 Differential operators on the base affine space and a study of g-modules, in 'Lie Groups And Their Representations', Adam Hilger, London, 1975. | Zbl 0338.58019
, and :2 Homomorphisms between generalized Verma modules, Dissertation, Yale University, 1982. | Zbl 0568.17004
:3 Intertwining operators between holomorphically induced modules, Pac. J. Math. 124 (1986), 73-84. | MR 850667 | Zbl 0632.22011
and :4 A multiplicity one theorem for holomorphically induced representations, Math. Z. 192 (1986), 265-282. | MR 840829 | Zbl 0598.22009
and :5 Gradient-type differential operators and unitary highest weight representations of SU(p, q), J. Funct. Anal. 81 (1988), 100-125. | MR 967893 | Zbl 0678.22004
and :6 Differential operators and highest weight representations, Memoirs of the A.M.S. #455 (1991). | MR 1081660 | Zbl 0759.22015
, and :7 Some characterizations of the Bruhat ordering on a Coxeter group and characterization of the relative Möbius function, Invent. Math. 39 (1977), 187-198. | MR 435249 | Zbl 0333.20041 | Zbl 0346.20032
:8 A classification of unitary highest weight modules, in Representation Theory Of Reductive Groups, P.C. Trombi (eds.) (1983), 97-143. | MR 733809 | Zbl 0535.22012
, and :9 An intrinsic analysis of unitarizable highest weight modules, Preprint 1990. | MR 1081264 | Zbl 0725.17009
and :10 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 644829 | Zbl 0492.22012
and :11 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 0072.01702
,12 Covariant differential operators, in Group Theoretical Methods In Physics, Istanbul 1982, Springer Lecture Notes in Physics 180, 1983. | MR 724940 | Zbl 0529.22015
and :13 Wave and Dirac operators and representations of the conformal group, J. Funct. Anal. 24 (1977), 52-106. | MR 439995 | Zbl 0361.22012
and :14 Restrictions and expansions of holomorphic representations, J. Funct. Anal. 34 (1979), 29-53. | MR 551108 | Zbl 0433.22011
and :15 On singular holomorphic representations, Invent. Math. 62 (1980), 67-78. | MR 595582 | Zbl 0466.22016
:16 The last possible place of unitarity for certain highest weight modules, Math. Ann. 256 (1981), 439-447. | MR 628225 | Zbl 0478.22007
:17 Hermitian symmetric spaces and their unitary highest weight modules, J. Funct. Anal. 52 (1983), 385-412. | MR 712588 | Zbl 0517.22014
:18 Basic covariant differential operators on hermitian symmetric spaces, Ann. scient. Èc. Norm. Sup. 18 (1985), 421-436. | Numdam | MR 826101 | Zbl 0619.32022
:19 The Representation Theory of the Symmetric Groups', Springer Lecture Notes in Math. #682, Springer Verlag, Berlin-Heidelberg- New York 1978. | Zbl 0393.20009
: '20 Annihilators and associated varieties of unitary highest weight modules, Preprint 1990, To appear in Ann. scient. Èc. Norm. Sup. | Numdam | MR 1152612 | Zbl 0752.17007
:21 On the Segal-Shale-Weil representation and harmonic polynomials, Invent. Math. 44 (1978), 1-47. | MR 463359 | Zbl 0375.22009
and :22 Limits of holomorphic discrete series, J. Funct. Anal. 9 (1972), 375-409. | MR 299726 | Zbl 0226.22010
and :23 All unitary ray representations of the conformal group SU(2,2) with positive energy, Comm. Math. Phys. 55 (1977), 1-28. | MR 447493 | Zbl 0352.22012
:24 Criteria for the unitarizability of some highest weight modules, Proc. Indian Acad. Sci. 89 (1980), 1-24. | MR 573381 | Zbl 0434.22011
:25 Analytic continuation of the holomorphic discrete series of a semi-simple Lie group, Acta Math. 136 (1976), 1-59. | MR 480883 | Zbl 0356.32020
and :26 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 309464 | Zbl 0239.46035
:27 Die Randwerte holomorpher Funktionen auf hermitesch symmetrischen Räumen, Invent. Math. 9 (1969), 61-80. | MR 259164 | Zbl 0219.32013
:28 Analytic continuation of the holomorphic discrete series II, Trans. Amer. Math, Soc. 260 (1980), 563-573. | MR 574799 | Zbl 0439.22017
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