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