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

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