Hypergroups arising from characters of a compact group and its subgroup

TL;DR

This paper explores a hypergroup structure derived from the irreducible characters of a compact group and its finite index subgroup, using induced and restricted representations to define convolution.

Contribution

It introduces a new hypergroup construction based on characters of a compact group and its subgroup, utilizing character theory and Frobenius reciprocity.

Findings

Defined a hypergroup structure from characters of a compact group and subgroup.

Used character formulae and Frobenius reciprocity to establish the hypergroup properties.

Abstract

The purpose of the present paper is to investigate a hypergroup arising from irreducible characters of a compact group G and a closed subgroup of G with finite index. The convolution of this hypergroup is introduced by inducing irreducible representations and by restricting irreducible representations. The method of proof relies on character formulae of induced representations of compact groups and of Frobenius' reciprocity theorem.