Representation theory of finite groups 1.1 Basic facts 1.2 Schur's lemma and the commutant 1.3 Characters and the projection formula 1.4 Permutation representations 1.5 The group algebra and the Fourier transform 1.6 Induced representations 2 The theory of Gelfand-Tsetlin bases 2.1 Algebras of conjugacy invariant functions 2.2 Gelfand-Tsetlin bases 3 The Okounkov-Vershik approach 3.1 The Young poset 3.2 The Young-Jucys-Murphy elements and a Gelfand-Tsetlin basis for S n 3.3 The spectrum of the Young-Jucys-Murphy elements and the branching graph of S n 3.4 The irreducible representation of S n 3.5 Skew representations and the Murnhagan-Nakayama rule 3.6 The Frobenius-Young correspondence 3.7 The Young rule
The first edition of the book (1993) was very well received, so that it was reprinted in 1995. This reviewer wrote the review on that (Zbl 0792.20006). Now in 2001, a second edition has been published. In comparison to the first edition, substantial additions have been made: In chapter 20 on Clifford's theorem on normal subgroups, in chapter 23 on the Brauer-Fowler theorem, in the former chapter 28 on remarks regarding Brauer's centralizer-of-an-involution techniques. Two new chapters have been added: chapter 28 on the character table of GL(2, p) and chapter 29 on permutations and characters.On the whole, this reviewer regards the second printing of the book as a gem in studying representation theory of finite groups.Reviewer: R.W.van der Waall (Amsterdam)
MSC:20C15 Ordinary representations and characters 20-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to group theory
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Keywords:ordinary representations; characters of groups; applications to molecular vibrations; introductory book; representation theory of finite groups; character calculations; groups of order p a q b ; GL(2, p); Clifford's theorem; Brauer-Fowler theorem; character tables
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