Transfer of Characters for Discrete Series Representations of the Unitary Groups in the Equal Rank Case via the Cauchy–Harish-Chandra integral

Abstract

Abstract As conjectured by Przebinda, the transfer of characters in the Howe’s correspondence should be obtained via the Cauchy–Harish-Chandra integral. In this paper, we prove that the conjecture holds for the dual pair $(\textrm{G} = \textrm{U}(p, q), \textrm{G}^{\prime} = \textrm{U}(r, s))$, $p+q = r+s$, starting with a discrete series representation $\Pi $ of $\widetilde{\textrm{U}}(p, q)$.