Generalizations of some integrals over the unitary group

TL;DR

This paper extends classical integrals over the unitary group to include general complex matrices using character expansion, with potential applications in random matrix theory and lattice gauge theory.

Contribution

It introduces a generalization of known unitary integrals to complex matrices via character expansion, expanding their applicability.

Findings

Generalized integrals involving complex matrices.

Potential applications in random matrix theory.

Relevance to lattice gauge theory.

Abstract

Using the character expansion method, we generalize several well-known integrals over the unitary group to the case where general complex matrices appear in the integrand. These integrals are of interest in the theory of random matrices and may also find applications in lattice gauge theory.