An intrinsic classification of the unitarizable highest weight modules as well as their associated varieties
Compositio Mathematica (1996)
- Volume: 101, Issue: 3, page 313-352
- ISSN: 0010-437X
Access Full Article
topHow to cite
topJakobsen, Hans Plesner. "An intrinsic classification of the unitarizable highest weight modules as well as their associated varieties." Compositio Mathematica 101.3 (1996): 313-352. <http://eudml.org/doc/90445>.
@article{Jakobsen1996,
author = {Jakobsen, Hans Plesner},
journal = {Compositio Mathematica},
keywords = {unitarizability; Bernstein-Gelfand-Gelfand theorem; hermitian symmetric space; holomorphic automorphisms; unitarizable highest weight representations; complexified Lie algebra; maximal torus; Verma module; Shapovalov form; associated varieties},
language = {eng},
number = {3},
pages = {313-352},
publisher = {Kluwer Academic Publishers},
title = {An intrinsic classification of the unitarizable highest weight modules as well as their associated varieties},
url = {http://eudml.org/doc/90445},
volume = {101},
year = {1996},
}
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
PB - Kluwer Academic Publishers
VL - 101
IS - 3
SP - 313
EP - 352
LA - eng
KW - unitarizability; Bernstein-Gelfand-Gelfand theorem; hermitian symmetric space; holomorphic automorphisms; unitarizable highest weight representations; complexified Lie algebra; maximal torus; Verma module; Shapovalov form; associated varieties
UR - http://eudml.org/doc/90445
ER -
References
top- 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. Zbl0338.58019
- 2 Boe, B.: Homomorphisms between generalized Verma modules, Dissertation, Yale University, 1982. Zbl0568.17004
- 3 Boe, B. and Collingwood, D.: Intertwining operators between holomorphically induced modules, Pac. J. Math.124 (1986), 73-84. Zbl0632.22011MR850667
- 4 Boe, B. and Collingwood, D.: A multiplicity one theorem for holomorphically induced representations, Math. Z.192 (1986), 265-282. Zbl0598.22009MR840829
- 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. Zbl0678.22004MR967893
- 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). Zbl0759.22015MR1081660
- 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. Zbl0333.20041MR435249
- 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. Zbl0535.22012MR733809
- 9 Enright, T.J. and Joseph, A.: An intrinsic analysis of unitarizable highest weight modules, Preprint 1990. Zbl0725.17009MR1081264
- 10 Enright, T.J. and Parthasarathy, R.: A proof of a conjecture of Kashiwara and Vergne, in Non-commutative Harmonic Analysis, Marseille-Luminy1980, Springer Lecture Notes in Mathematics, 880 (1981), 74-90. Zbl0492.22012MR644829
- 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. Zbl0072.01702
- 12 Harris, M. and Jakobsen, H.P.: Covariant differential operators, in Group Theoretical Methods In Physics, Istanbul1982, Springer Lecture Notes in Physics180, 1983. Zbl0529.22015MR724940
- 13 Jakobsen, H.P. and Vergne, M.: Wave and Dirac operators and representations of the conformal group, J. Funct. Anal.24 (1977), 52-106. Zbl0361.22012MR439995
- 14 Jakobsen, H.P. and Vergne, M.: Restrictions and expansions of holomorphic representations, J. Funct. Anal.34 (1979), 29-53. Zbl0433.22011MR551108
- 15 Jakobsen, H.P.: On singular holomorphic representations, Invent. Math.62 (1980), 67-78. Zbl0466.22016MR595582
- 16 Jakobsen, H.P.: The last possible place of unitarity for certain highest weight modules, Math. Ann.256 (1981), 439-447. Zbl0478.22007MR628225
- 17 Jakobsen, H.P.: Hermitian symmetric spaces and their unitary highest weight modules, J. Funct. Anal.52 (1983), 385-412. Zbl0517.22014MR712588
- 18 Jakobsen, H.P.: Basic covariant differential operators on hermitian symmetric spaces, Ann. scient. Èc. Norm. Sup.18 (1985), 421-436. Zbl0619.32022MR826101
- 19 James, G.D.: 'The Representation Theory of the Symmetric Groups', Springer Lecture Notes in Math. #682, Springer Verlag, Berlin-Heidelberg- New York1978. Zbl0393.20009
- 20 Joseph, A.: Annihilators and associated varieties of unitary highest weight modules, Preprint 1990, To appear in Ann. scient. Èc. Norm. Sup. Zbl0752.17007MR1152612
- 21 Kashiwara, M. and Vergne, M.: On the Segal-Shale-Weil representation and harmonic polynomials, Invent. Math.44 (1978), 1-47. Zbl0375.22009MR463359
- 22 Knapp, A. and Okamoto, K.: Limits of holomorphic discrete series, J. Funct. Anal.9 (1972), 375-409. Zbl0226.22010MR299726
- 23 Mack, G.: All unitary ray representations of the conformal group SU(2,2) with positive energy, Comm. Math. Phys.55 (1977), 1-28. Zbl0352.22012MR447493
- 24 Parthasarathy, K.R.: Criteria for the unitarizability of some highest weight modules, Proc. Indian Acad. Sci.89 (1980), 1-24. Zbl0434.22011MR573381
- 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. Zbl0356.32020MR480883
- 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. Zbl0239.46035MR309464
- 27 Schmid, W.: Die Randwerte holomorpher Funktionen auf hermitesch symmetrischen Räumen, Invent. Math.9 (1969), 61-80. Zbl0219.32013MR259164
- 28 Wallach, N.: Analytic continuation of the holomorphic discrete series II, Trans. Amer. Math, Soc. 260 (1980), 563-573. Zbl0439.22017
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.