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On the unitary dual of 
Author(s):
Alfredo
O.
Brega
Journal:
Trans. Amer. Math. Soc.
351
(1999),
403-415.
MSC (1991):
Primary 22E46
MathSciNet review:
1473432
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Abstract:
In this paper we begin a systematic study of the unitarity question for genuine representations of the group  . The main result is that we find a class of unitary representations (mostly isolated) analogous to the special unipotent representations defined by D. Barbasch and D. Vogan. In particular the full unitary dual of  should be obtainable from this set by complementary series.
References:
- [B]
- Barbasch, D.: ``The unitary dual for complex classical Lie groups'', Invent. Math. 96, 103-176 (1989). MR 90c:22044
- [BV1]
- Barbasch, D., Vogan, D.: ``Unipotent representations of complex semisimple Lie groups'', Ann. Math. 121, 41-110 (1985). MR 86i:22031
- [BV2]
- Barbasch, D., Vogan, D.: ``The local structure of characters'', J. Funct. Anal. 37, 27-55 (1980). MR 82e:22024
- [D]
- Duflo, M.: ``Representations irreductibles des groupes semisimples complexes'', Lect. Notes in Math., Vol. 497, pp. 26-88, Springer-Verlag 1975. MR 53:3198
- [H]
- Howe, R.: ``Wavefront sets of representations of Lie groups'', in ``Automorphic Forms, Representation Theory and Arithmetic'', Tata Inst. Fund. Res. Studies in Math. 10, Tata Inst. Fund. Res., Bombay 1981. MR 83c:22014
- [L1]
- Lusztig, G.: ``A class of irreducible representations of a Weyl group'', Proc. Nederl. Akad., Series A 82, 323-335 (1979). MR 81a:20052
- [L2]
- Lusztig, G.: ``Characters of a Reductive Group over a Finite Field'', Princeton University Press, Princeton, New Jersey, 1984. MR 86j:20038
- [SV]
- Speh, B., Vogan, D.: ``Reducibility of generalized principal series representations'', Acta Math. 145 (1980), 227-299. MR 82c:22018
- [V1]
- Vogan, D.: ``The unitary dual of
 '', Invent. Math. 83, 449-505 (1986). MR 87i:22042 - [V2]
- Vogan, D.: ``Unitarizability of certain series of representations'', Ann. of Math. 120 (1984), 141-187. MR 86h:22028
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Additional Information:
Alfredo
O.
Brega
Affiliation:
Facultad de Matemática, Astronomía y Física (Fa.M.A.F), Universidad Nacional de Córdoba, Ciudad Universitaria, 5000 - Córdoba, Argentina
Email:
brega@mate.uncor.edu
DOI:
10.1090/S0002-9947-99-02173-X
PII:
S 0002-9947(99)02173-X
Keywords:
Special unipotent representations,
unitary dual,
Spin groups.
Received by editor(s):
April 29, 1996
Received by editor(s) in revised form:
February 6, 1997
Additional Notes:
Research partially supported by CONICOR, SECYT-UNC and SECITECOR (Argentina) grants.
Copyright of article:
Copyright
1999,
American Mathematical Society
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