Cauchy Identities for the Characters of the Compact Classical Groups

TL;DR

This paper develops new Cauchy identities for characters of compact classical groups, extending known identities for unitary groups, with potential applications in statistical hypothesis testing.

Contribution

It introduces generalized Cauchy identities for classical group characters, broadening the scope of symmetric function theory in statistical contexts.

Findings

Derived new identities for classical group characters

Extended the Cauchy identity beyond unitary groups

Suggested applications in statistical hypothesis testing

Abstract

Motivated by statistical applications, this paper introduces Cauchy identities for characters of the compact classical groups. These identities generalize the well-known Cauchy identity for characters of the unitary group, which are Schur functions of symmetric function theory. Application to statistical hypothesis testing is briefly sketched.