Representation theory of finite groups. An introductory approach.
type: Item
instance of: scholarly article
title: Representation theory of finite groups. An introductory approach.
zbMATH Open document ID: 1243.20001
DOI: 10.1007/978-1-4614-0776-8
author: Benjamin Steinberg
published in: Universitext
publication date: 2011-08-29T00:00:00Z
review text: The required background to this introductory course on group representations is on the level of linear algebra, group theory and some ring theory. Module theory and Wedderburn theory are deliberately omitted, as well as tensor products. On the other hand, an approach based on discrete Fourier analysis is taken. Included are (mainly): character theory, graph algebras, Fourier analysis, Burnside's \(pq\)-theorem, permutation representations, induced representations, Mackey's theorem. The reviewer regards the outlooks of the general representation theory of finite groups, as presented here with little excursions to the representation theory of symmetric groups, random walks on finite groups, finite stochastics and representation theory, spectral theory of graphs, as enhancing extras. Also a section on card shuffling, in particular the riffle shuffle, is here to find. Summarising, the book under review is a welcome one for students at an advanced undergraduate or introductory graduate level course, also for those people like physicists, statisticians and non-algebraically oriented mathematicians who need representation theory in their work. To close this review, let us mention that each chapter contains some good exercises.
Mathematics Subject Classification ID: 20-01
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20C30
Mathematics Subject Classification ID: 20P05
zbMATH DE Number: 5944107
zbMATH Keywords: representation theory of finite groups
zbMATH Keywords: Fourier analysis on finite groups
zbMATH Keywords: card shuffling
zbMATH Keywords: symmetric groups
zbMATH Keywords: probability and random walks on finite groups
reviewed by: Robert W. van der Waall
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-1-4614-0776-8
OpenAlex ID: W2503161983
description: scientific article; zbMATH DE number 5944107