**Graduate Studies in Mathematics**

Volume: 144;
2012;
302 pp;
Hardcover

MSC: Primary 17;

Print ISBN: 978-0-8218-9118-6

Product Code: GSM/144

List Price: $64.00

Individual Member Price: $51.20

**Electronic ISBN: 978-0-8218-9447-7
Product Code: GSM/144.E**

List Price: $64.00

Individual Member Price: $51.20

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#### Supplemental Materials

# Dualities and Representations of Lie Superalgebras

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*Shun-Jen Cheng; Weiqiang Wang*

This book gives a systematic account of the structure and representation theory of finite-dimensional complex Lie superalgebras of classical type and serves as a good introduction to representation theory of Lie superalgebras. Several folklore results are rigorously proved (and occasionally corrected in detail), sometimes with new proofs. Three important dualities are presented in the book, with the unifying theme of determining irreducible characters of Lie superalgebras. In order of increasing sophistication, they are Schur duality, Howe duality, and super duality. The combinatorics of symmetric functions is developed as needed in connections to Harish-Chandra homomorphism as well as irreducible characters for Lie superalgebras. Schur-Sergeev duality for the queer Lie superalgebra is presented from scratch with complete detail. Howe duality for Lie superalgebras is presented in book form for the first time. Super duality is a new approach developed in the past few years toward understanding the Bernstein-Gelfand-Gelfand category of modules for classical Lie superalgebras. Super duality relates the representation theory of classical Lie superalgebras directly to the representation theory of classical Lie algebras and thus gives a solution to the irreducible character problem of Lie superalgebras via the Kazhdan-Lusztig polynomials of classical Lie algebras.

#### Table of Contents

# Table of Contents

## Dualities and Representations of Lie Superalgebras

- Cover Cover11 free
- Title page iii4 free
- Contents vii8 free
- Preface xiii14 free
- Chapter 1. Lie superalgebra ABC 120 free
- Chapter 2. Finite-dimensional modules 4362
- Chapter 3. Schur duality 91110
- Chapter 4. Classical invariant theory 131150
- Chapter 5. Howe duality 151170
- Chapter 6. Super duality 205224
- Appendix A. Symmetric functions 261280
- Bibliography 291310
- Index 299318 free
- Back Cover Back Cover1322

#### Readership

Graduate students and research mathematicians interested in Lie algebras, Lie superalgebras, representation theory, mathematical physics, and especially supersymmetry.