On the unitary dual of 𝑆𝑝𝑖𝑛(2𝑛,ℂ)

Brega, Alfredo

doi:10.1090/S0002-9947-99-02173-X

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.

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