Representation theory is concerned with the ways of writing a groupas a group of matrices. Not only is the theory beautiful in its own right，but it also provides one of the keys to a proper understanding of finitegroups. For example， it is often vital to have a concrete description of aparticular group； this is achieved by finding a representation of thegroup as a group of matrices. Moreover， by studying the differentrepresentations of the group， it is possible to prove results which lieoutside the framework of representation theory. One simple example： allgroups of order p2 （where p is a prime number） are abelian； this can beshown quickly using only group theory， but it is also a consequence ofbasic results about representations.
作者簡介
暫缺《群的表示與群的特征》作者簡介
圖書目錄
Preface 1 Groups and homomorphisms 2 Vector spaces and linear transformations 3 Group representations 4 FG-modules 5 FG-submodules and reducibility 6 Group algebras 7 FG-homomorphisms 8 Maschke's Theorem 9 Schur's Lemma 10 Irreducible modules and the group algebra 11 More on the group algebra 12 Conjugacy classes 13 Characters 14 Inner products of characters 15 The number of irreducible characters 16 Character tables and orthogonality relations 17 Normal subgroups and lifted characters 18 Some elementary character tables 19 Tensor products 20 Restriction to a subgroup 21 Induced modules and characters 22 Algebraic integers 23 Real representations 24 Summary of properties of character tables 25 Characters of groups of order pq 26 Characters of some p-groups 27 Character table of the simple group of order 168 28 Character table of GL(2, q) 29 Permutations and characters 30 Applications to group theory 31 Burnside's Theorem 32 An application of representation theory to molecular vibration Solutions to exercises Bibliography Index
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