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Transactions of the American Mathematical Society

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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
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 $ 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.


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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