Representations and Characters of GroupsThis book provides a modern introduction to the representation theory of finite groups. |
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This is the best book to know what "Representation" actually means....
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Simple and Excellent book on representations of groups
Contents
Groups and homomorphisms | 1 |
Vector spaces and linear transformations | 14 |
Group representations | 30 |
FGmodules | 38 |
FGsubmodules and reducibility | 49 |
Group algebras | 53 |
FGhomomorphisms | 61 |
Maschkes Theorem | 70 |
Tensor products | 188 |
Restriction to a subgroup | 210 |
Induced modules and characters | 224 |
Algebraic integers | 244 |
Real representations | 263 |
Summary of properties of character tables | 283 |
Characters of groups of order pq | 288 |
Characters of some pgroups | 298 |
Schurs Lemma | 78 |
Irreducible modules and the group algebra | 89 |
More on the group algebra | 95 |
Conjugacy classes | 104 |
Characters | 117 |
Inner products of characters | 133 |
The number of irreducible characters | 152 |
Character tables and orthogonality relations | 159 |
Normal subgroups and lifted characters | 168 |
Some elementary character tables | 179 |
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Common terms and phrases
abelian Assume basis calculate called CG-homomorphism CG-submodule Chapter character of G character table Check classes of G column complete conjugacy classes conjugate consider construct contains Corollary corresponding deduce define Definition denote determine direct sum divides eigenvalue eigenvectors elements elements of G endomorphism entries equal equation equivalent Example Exercise exists express fact faithful finite group follows function given gives group G group of order Hence Homco homomorphism identity integer invertible irreducible CG-module irreducible characters isomorphic Lemma Let G linear characters matrix modes module multiplication non-zero normal subgroup Note obtain orthogonality relations permutation prime Proof Proposition Prove reducible representation representatives result rotation satisfies Show solution subgroup of G Suppose symmetric table of G Theorem theory values vector space write
References to this book
Bibliographic information
| Title | Representations and Characters of Groups Cambridge mathematical textbooks Representations and Characters of Groups, Gordon Douglas James |
| Authors | Gordon James, Martin W. Liebeck, Martin Liebeck |
| Edition | illustrated, reprint, revised |
| Publisher | Cambridge University Press, 2001 |
| ISBN | 052100392X, 9780521003926 |
| Length | 458 pages |
| Subjects | › › Mathematics / Algebra / General Mathematics / Group Theory |
| Export Citation | BiBTeX EndNote RefMan |