Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

On the unitary dual of $ Spin (2 n, \mathbb{C})$


Author: Alfredo O. Brega
Journal: Trans. Amer. Math. Soc. 351 (1999), 403-415
MSC (1991): Primary 22E46
DOI: https://doi.org/10.1090/S0002-9947-99-02173-X
MathSciNet review: 1473432
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we begin a systematic study of the unitarity question for genuine representations of the group $ Spin (2 n, \mathbb{C})$. 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 $ Spin (2 n, \mathbb{C})$ should be obtainable from this set by complementary series.


References [Enhancements On Off] (What's this?)

  • [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 $G L(n) $'', Invent. Math. 83, 449-505 (1986). MR 87i:22042

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 22E46

Retrieve articles in all journals with MSC (1991): 22E46


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: https://doi.org/10.1090/S0002-9947-99-02173-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.
Article copyright: © Copyright 1999 American Mathematical Society

American Mathematical Society