Hypergroups Related to a Pair of Compact Hypergroups

TL;DR

This paper explores a new hypergroup construction derived from irreducible characters of a compact hypergroup and its subhypergroup, focusing on convolution operations via induction and restriction.

Contribution

It introduces a hypergroup associated with a pair of compact hypergroups using induced and restricted irreducible characters, expanding hypergroup theory.

Findings

Defined a hypergroup structure via induced and restricted characters

Established properties of the convolution operation in this hypergroup

Connected the structure to admissible hypergroup pairs

Abstract

The purpose of the present paper is to investigate a hypergroup associated with irreducible characters of a compact hypergroup $H$ and a closed subhypergroup $H_0$ of $H$ with $|H/H_0|< +\infty$. The convolution of this hypergroup is introduced by inducing irreducible characters of $H_0$ to $H$ and by restricting irreducible characters of $H$ to $H_0$. The method of proof relies on the notion of an induced character and an admissible hypergroup pair.