On the unitary dual of some classical Lie groups
Compositio Mathematica (1988)
- Volume: 68, Issue: 3, page 251-303
- ISSN: 0010-437X
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topSalamanca Riba, Susana. "On the unitary dual of some classical Lie groups." Compositio Mathematica 68.3 (1988): 251-303. <http://eudml.org/doc/89938>.
@article{SalamancaRiba1988,
author = {Salamanca Riba, Susana},
journal = {Compositio Mathematica},
keywords = {unitary dual; fundamental K-type; complementary series; real groups; special unipotent representations; integral infinitesimal character; real reductive Lie group; irreducible unitary Harish-Chandra module; irreducible unitary representations; relative Lie algebra cohomology},
language = {eng},
number = {3},
pages = {251-303},
publisher = {Kluwer Academic Publishers},
title = {On the unitary dual of some classical Lie groups},
url = {http://eudml.org/doc/89938},
volume = {68},
year = {1988},
}
TY - JOUR
AU - Salamanca Riba, Susana
TI - On the unitary dual of some classical Lie groups
JO - Compositio Mathematica
PY - 1988
PB - Kluwer Academic Publishers
VL - 68
IS - 3
SP - 251
EP - 303
LA - eng
KW - unitary dual; fundamental K-type; complementary series; real groups; special unipotent representations; integral infinitesimal character; real reductive Lie group; irreducible unitary Harish-Chandra module; irreducible unitary representations; relative Lie algebra cohomology
UR - http://eudml.org/doc/89938
ER -
References
top- J. Adams: Discrete spectrum of the dual pair (0(p, q), Sp(2m)). Invent. Math.74 (1983) 449-475. Zbl0561.22011MR724015
- J. Adams: Unitary highest weight modules. Advances in Math.63 (1987) 113-137. Zbl0623.22014MR872349
- J. Arthur: On some problems suggested by the trace formula. SLN1041 (1984) 1-50. Zbl0541.22011MR748504
- M.W. Baldoni Silva and D. Barbasch: The unitary spectrum for real rank one groups. Invent. Math.72 (1983) 27-55. Zbl0561.22009MR696689
- D. Barbasch: Unipotent representations for complex semisimple groups II. Preprint (1987). Zbl0629.22007MR897538
- D. Barbasch and D. Vogan: Unipotent representations for complex semisimple groups. Ann. Math.121 (1985) 41-110. Zbl0582.22007MR782556
- A. Borel and N. Wallach: Continuous cohomology, discrete subgroups and representations of reductive groups. Annals of Mathematics Studies Vol. 94. Princeton University Press (1980). Zbl0443.22010MR554917
- J. Dixmier: Enveloping Algebras. North Holland Publishing Co., Amsterdam, N.Y., Oxford (1977). Zbl0339.17007MR498740
- M. Duflo and M. Vergne: Sur le foncteur de Zuckerman. C.R. Acad. Sci. Paris, t. 304 Serie I, no. 16 (1987) pp. 467-469. Zbl0617.17007MR894570
- T.J. Enright: Relative Lie algebra cohomology and unitary representations of complex Lie groups. Duke Math. J.46 (1979) 513-525. Zbl0427.22010MR544243
- T.J. Enright: Unitary representations for two real forms of a semisimple Lie algebra: a theory of comparison. In: Proc. Special Year in Harmonic Analysis, University of Maryland Lecture Notes in Math. Vol. 1024 (1984) pp. 1-29. Springer-Verlag, Berlin-Heidelberg -New York-Tokyo. Zbl0531.22012MR727848
- T.J. Enright and N.R. Wallach: Notes on homological algebra and representations of Lie algebras. Duke Math. J.47 (1980) 1-15. Zbl0429.17012MR563362
- Harish-Chandra: Representations of semisimple Lie groups I. Trans. AMS75 (1953) 185-243. Zbl0051.34002MR56610
- A.W. Knapp and D.A. Vogan Jr: Cohomological induction and unitary representations, Preprint.
- A. Knapp and G. Zuckerman: Classification theorems for representations of semisimple Lie groups. In: Non-Commutative Harmonic Analysis. Lecture Notes in Math. Vol. 587 (1976) pp. 138-159. Zbl0353.22011MR476923
- R. Langlands: (1973) On the classification of irreducible representations of real algebraic groups. Mimeographed notes, Institute for Advanced Study (1973).
- S. Salamanca Riba: On unitary representations with regular infinitesimal character. Thesis dissertation, Massachusetts Institute of Technology, Cambridge, Massachusetts (1986).
- W. Schmid: On the characters of discrete series (the Hermitian symmetric case). Inventiones Math.30 (1975) 47-144. Zbl0324.22007MR396854
- B. Speh: Unitary representations of SL(n, R) and the cohomology of congruence subgroups. In: J. Carmona and M. Vergne (Eds.) Non-Commutative Harmonic Analysis and Lie groups. Lecture Notes in Math. Vol. 880 (1981) pp. 483-505. Zbl0516.22008MR644844
- B. Speh and D. Vogan: Reducibility of generalized principal series representations. Acta Math.145 (1980) 227-229. Zbl0457.22011MR590291
- D. Vogan: The algebraic structure of the representations of semisimple Lie groups I. Ann. Math.109 (1979) 1-60. Zbl0424.22010MR519352
- D. Vogan: Representations of Real Reductive Lie Groups. Birkhauser, Boston-Basel- Stuttgart (1981). Zbl0469.22012MR632407
- D. Vogan: Unitarizability of certain series of representations. Annals Math.120 (1984) 141-187. Zbl0561.22010MR750719
- D. Vogan: The unitary dual of GL(n) over an Archimedian field. Inv. Math.83 (1986) 449-505. Zbl0598.22008MR827363
- D. Vogan and G. Zuckerman: Unitary representations with non-zero cohomology. Compositio Mathematica53 (1984) 51-90. Zbl0692.22008MR762307
- D. Wigner: Sur l'homologic relative des algèbres de Lie et une conjecture de Zuckerman. C.R. Acad. Sci. Paris, t 305, Série I (1987) pp. 59-62. Zbl0617.17006MR901135
- G. Zuckerman: On construction of representations by derived factors. Handwritten Notes (1977).
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