On the unitary dual of $Spin(2n,\mathbb C)$
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- by Alfredo O. Brega PDF
- Trans. Amer. Math. Soc. 351 (1999), 403-415 Request permission
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
-
D. Barbasch. The unitary dual for complex classical Lie groups, Invent. Math. 96, 103–176 (1989). MR 90c:22044.
- Dan Barbasch and David A. Vogan Jr., Unipotent representations of complex semisimple groups, Ann. of Math. (2) 121 (1985), no. 1, 41–110. MR 782556, DOI 10.2307/1971193
- Dan Barbasch and David A. Vogan Jr., The local structure of characters, J. Functional Analysis 37 (1980), no. 1, 27–55. MR 576644, DOI 10.1016/0022-1236(80)90026-9
- Michel Duflo, Représentations irréductibles des groupes semi-simples complexes, Analyse harmonique sur les groupes de Lie (Sém., Nancy-Strasbourg, 1973–75), Lecture Notes in Math., Vol. 497, Springer, Berlin, 1975, pp. 26–88 (French). MR 0399353
- Roger Howe, Wave front sets of representations of Lie groups, Automorphic forms, representation theory and arithmetic (Bombay, 1979), Tata Inst. Fund. Res. Studies in Math., vol. 10, Tata Institute of Fundamental Research, Bombay, 1981, pp. 117–140. MR 633659
- G. Lusztig, A class of irreducible representations of a Weyl group, Nederl. Akad. Wetensch. Indag. Math. 41 (1979), no. 3, 323–335. MR 546372, DOI 10.1016/1385-7258(79)90036-2
- George Lusztig, Characters of reductive groups over a finite field, Annals of Mathematics Studies, vol. 107, Princeton University Press, Princeton, NJ, 1984. MR 742472, DOI 10.1515/9781400881772
- Birgit Speh and David A. Vogan Jr., Reducibility of generalized principal series representations, Acta Math. 145 (1980), no. 3-4, 227–299. MR 590291, DOI 10.1007/BF02414191
- David A. Vogan Jr., The unitary dual of $\textrm {GL}(n)$ over an Archimedean field, Invent. Math. 83 (1986), no. 3, 449–505. MR 827363, DOI 10.1007/BF01394418
- David A. Vogan Jr., Unitarizability of certain series of representations, Ann. of Math. (2) 120 (1984), no. 1, 141–187. MR 750719, DOI 10.2307/2007074
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
- 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 1999 American Mathematical Society
- 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