Characters of irreducible unitary representations of 𝑈(𝑛,𝑛+1) via double lifting from 𝑈(1)

Merino, Allan

doi:10.1090/ert/597

Characters of irreducible unitary representations of $\operatorname {U}(n, n+1)$ via double lifting from $\operatorname {U}(1)$
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Represent. Theory 26 (2022), 325-369 Request permission

Abstract:

In this paper, we obtained character formulas of irreducible unitary representations of $U(n, n+1)$ by using Howe’s correspondence and the Cauchy–Harish-Chandra integral. The representations of $U(n, n+1)$ we are dealing with are obtained from a double lifting of a representation of $U(1)$ via the dual pairs $(U(1), U(1, 1))$ and $(U(1, 1), U(n, n+1))$.

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