Composition series for analytic continuations of holomorphic discrete series representations of 𝑆𝑈(𝑛,𝑛)

Ørsted, Bent

doi:10.1090/S0002-9947-1980-0574799-X

Composition series for analytic continuations of holomorphic discrete series representations of $\textrm {SU}(n, n)$
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Trans. Amer. Math. Soc. 260 (1980), 563-573 Request permission

Abstract:

We study a certain family of holomorphic discrete series representations of the semisimple Lie group $G = SU(n, n)$ and the corresponding analytic continuation in the inducing parameter $\lambda$. At the values of $\lambda$ where the representations become reducible, we compute the composition series in terms of a Peter-Weyl basis on the Shilov boundary of the Hermitian symmetric space for G.

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The classical groups