Representation Theory A First Course

ISBN-10: 0387974954

ISBN-13: 9780387974958

Edition: 3rd 2004

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Description: The primary goal of these lectures is to introduce a beginner to the finite-dimensional representations of Lie groups and Lie algebras. Intended to serve non-specialists, the concentration of the text is on examples. The general theory is developed sparingly, and then mainly as useful and unifying language to describe phenomena already encountered in concrete cases. The book begins with a brief tour through representation theory of finite groups, with emphasis determined by what is useful for Lie groups. The focus then turns to Lie groups and Lie algebras and finally to the heart of the course: working out the finite dimensional representations of the classical groups. The goal of the last portion of the book is to make a bridge between the example-oriented approach of the earlier parts and the general theory.

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Book details

List price: $59.95
Edition: 3rd
Copyright year: 2004
Publisher: Springer
Publication date: 7/30/1999
Binding: Paperback
Pages: 551
Size: 6.25" wide x 9.50" long x 1.00" tall
Weight: 1.738
Language: English

Finite Groups
Representations of Finite Groups
Characters
Examples; Induced Representations; Groups Algebras; Real Representations
Representations of Ed: Young Diagrams and Frobenius's Character Formula
Representation of Ud and GL2 and (Fq)
Weyl's Construction
Lie Groups and Lie Algebras
Lie Groups
Lie Algebras and Lie Groups
Initial Classification of Lie Algebras
Lie Algebras in Dimensions One, Two, and Three
Representation of sI2 C
Representation of sI3 C, Part I
Representation of sI3 C, II: Mainly Lots of Examples
The Classical Lie Algebras and Their Representations
The General Set-up: Analyzing the Structure and Representations of an Arbitrary Semi simple Lie Algebra
SI4 C and sIn C
Symplectic Lie Algebras
Sp6C and sp2n C
Orthogonal Lie Algebras
So6 C, so7 C, and som C
Spin Representations of so m C
Lie Theory
The Classification of Complex Simple Lie Algebras
G2 and Other Exceptional Lie Algebras
Complex Lie Groups; Characters
Weyl Character Formula
More Character Formulas
Real Lie Algebras and Lie Groups
Appendices A - F
Hints
Answers
References
Bibliography
Index of Symbols
Index
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