Representation theory of finite groups. An introductory approach.
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.
probability and random walks on finite groups
scientific article; zbMATH DE number 5944107