Clebsch-Gordan series, the inverse of a Cartan matrix and $\eta$-invariants

TL;DR

This paper explores formulas connecting the inverse of a Cartan matrix with algebraic and geometric invariants in finite group representations, providing new insights into their relationships.

Contribution

It introduces formulas linking the inverse Cartan matrix to invariants of finite group representations, enhancing understanding of their algebraic and geometric properties.

Findings

Derived formulas relating inverse Cartan matrices to group invariants

Established connections between algebraic and geometric aspects of representations

Provided new tools for analyzing finite group representations

Abstract

We prove some formulas relating the inverse of a Cartan matrix with algebraic and geometric invariants of finite group representations.