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

TL;DR

This paper derives character formulas for irreducible unitary representations of the group U(n, n+1) using Howe's correspondence and integral techniques, based on a double lifting process from U(1).

Contribution

It introduces a novel method to compute characters of U(n, n+1) representations via double lifting from U(1) using Howe's correspondence.

Findings

Derived explicit character formulas for U(n, n+1) representations.

Connected double lifting process with Howe's correspondence.

Applied Cauchy--Harish-Chandra integral in representation analysis.

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 $(U(1, 1), U(n, n+1))$.