Character expansion of matrix integrals

TL;DR

This paper explores the expansion of matrix integrals and tau functions into characters of orthogonal and symplectic groups, providing new insights into their structure and applications.

Contribution

It introduces character expansions for integrals over orthogonal and symplectic matrices, extending previous work on matrix integrals and tau functions.

Findings

Derived explicit character expansion formulas for orthogonal and symplectic matrix integrals.

Enhanced understanding of the structure of tau functions in terms of group characters.

Potential applications in mathematical physics and representation theory.

Abstract

We consider character expansion of tau functions and multiple integrals in characters of orhtogonal and symplectic groups. In particular we consider character expansions of integrals over orthogonal and over symplectic matrices.