Representation Theory A First Course

Name: Representation Theory A First Course
Availability: InStock
ISBN: 9780387974958

ISBN-10: 0387974954

ISBN-13: 9780387974958

Edition: 3rd 2004

Authors: William Fulton, Joe Harris

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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…

Book details

List price: $69.99
Edition: 3rd
Copyright year: 2004
Publisher: Springer New York
Publication date: 10/22/1991
Binding: Paperback
Pages: 551
Size: 6.10" wide x 9.25" long x 0.42" tall
Weight: 2.002




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