Hardcover ISBN:  9780821891186 
Product Code:  GSM/144 
302 pp 
List Price:  $68.00 
MAA Member Price:  $61.20 
AMS Member Price:  $54.40 
Electronic ISBN:  9780821894477 
Product Code:  GSM/144.E 
297 pp 
List Price:  $64.00 
MAA Member Price:  $57.60 
AMS Member Price:  $51.20 

Book DetailsGraduate Studies in MathematicsVolume: 144; 2012MSC: Primary 17;
This book gives a systematic account of the structure and representation theory of finitedimensional 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 HarishChandra homomorphism as well as irreducible characters for Lie superalgebras. SchurSergeev 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 BernsteinGelfandGelfand 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 KazhdanLusztig polynomials of classical Lie algebras.
ReadershipGraduate students and research mathematicians interested in Lie algebras, Lie superalgebras, representation theory, mathematical physics, and especially supersymmetry.

Table of Contents

Chapters

Chapter 1. Lie superalgebra ABC

Chapter 2. Finitedimensional modules

Chapter 3. Schur duality

Chapter 4. Classical invariant theory

Chapter 5. Howe duality

Chapter 6. Super duality

Appendix A. Symmetric functions


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This book gives a systematic account of the structure and representation theory of finitedimensional 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 HarishChandra homomorphism as well as irreducible characters for Lie superalgebras. SchurSergeev 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 BernsteinGelfandGelfand 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 KazhdanLusztig polynomials of classical Lie algebras.
Graduate students and research mathematicians interested in Lie algebras, Lie superalgebras, representation theory, mathematical physics, and especially supersymmetry.

Chapters

Chapter 1. Lie superalgebra ABC

Chapter 2. Finitedimensional modules

Chapter 3. Schur duality

Chapter 4. Classical invariant theory

Chapter 5. Howe duality

Chapter 6. Super duality

Appendix A. Symmetric functions