Dual space and hyperdimension of compact hypergroups

TL;DR

This paper explores the dual spaces and hyperdimensions of compact hypergroups, compares their representation theory with finite groups, and establishes a Heisenberg inequality for these structures.

Contribution

It provides new characterizations of dual spaces and hyperdimensions for specific classes of compact hypergroups and compares their representation theory with finite groups.

Findings

Characterized dual spaces of conjugacy classes of compact groups

Computed hyperdimensions of irreducible representations

Established a Heisenberg inequality for compact hypergroups

Abstract

We characterize dual spaces and compute hyperdimensions of irreducible representations for two classes of compact hypergroups namely conjugacy classes of compact groups and compact hypergroups constructed by joining compact and finite hypergroups. Also studying the representation theory of finite hypergroups, we highlight some interesting differences and similarities between the representation theories of finite hypergroups and finite groups. Finally, we compute the Heisenberg inequality for compact hypergroups.