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2016 | OriginalPaper | Chapter

5 Irreducible Representations

Author : Benjamin Steinberg

Published in: Representation Theory of Finite Monoids

Publisher: Springer International Publishing

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Abstract

Clifford-Munn-Ponizovskiĭ theory, developed in Clifford [Cli42], Munn [Mun55, Mun57b, Mun60], and Ponizovskiĭ [Pon58] (and in further detail in [LP69, RZ91]), gives a bijection between equivalence classes of irreducible representations of a finite monoid and equivalence classes of irreducible representations of its maximal subgroups (taken one per regular \(\mathcal{J}\)-class). We follow here the approach of [GMS09], using the techniques of Chapter 4 Let us commence by introducing formally the notion of a representation of a monoid.

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previous chapter 4 Recollement: The Theory of an Idempotent

next chapter 6 The Grothendieck Ring

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Title: 5 Irreducible Representations
Author: Benjamin Steinberg
Publisher: Springer International Publishing
Book: Representation Theory of Finite Monoids
Print ISBN: 978-3-319-43930-3

Electronic ISBN: 978-3-319-43932-7

Copyright Year: 2016
DOI: https://doi.org/10.1007/978-3-319-43932-7_5

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