Fusion rule algebras related to a pair of compact groups

TL;DR

This paper explores a fusion rule algebra constructed from irreducible characters of a compact group and its finite index subgroup, using induction and restriction of representations to define convolution.

Contribution

It introduces a new fusion rule algebra framework based on the interplay of irreducible representations between a compact group and its subgroup.

Findings

Defines a convolution operation via induction and restriction

Establishes properties of the fusion rule algebra

Connects the algebra to representation theory of compact groups

Abstract

The purpose of the present paper is to investigate a fusion rule algebra arising from irreducible characters of a compact group $G$ and a closed subgroup $G_0$ of $G$ with finite index. The convolution of this fusion rule algebra is introduced by inducing irreducible representations of $G_0$ to $G$ and by restricting irreducible representations of $G$ to $G_0$.