The sympathetic sceptics guide to semigroup representations

TL;DR

This paper provides an elementary introduction to finite semigroup representation theory, emphasizing the Clifford-Munn correspondence and illustrating concepts with naturally occurring examples.

Contribution

It offers a clear, accessible explanation of semigroup representations and highlights the connection to maximal subgroups, making the topic approachable for newcomers.

Findings

Clifford-Munn correspondence links semigroup and subgroup representations

Illustrates concepts with naturally occurring examples

Provides foundational understanding of finite semigroup representations

Abstract

This is an elementary introduction to the representation theory of finite semigroups. We illustrate the Clifford-Munn correspondence between the representations of a semigroup and the representations of its maximal subgroups. The emphasis throughout is on naturally occurring examples.