Representation Theory

by Fulton, William; Harris, Joe

• ISBN13: 9780387974958
• ISBN10: 0387974954
• Format: Paperback
• Copyright: 1991-09-01
• Publisher: Springer Nature

Summary

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.

Table of Contents

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

Table of Contents provided by Publisher. All Rights Reserved.