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Dualities and Representations of Lie Superalgebras

Shun-Jen Cheng Academia Sinica, Taipei, Taiwan
Weiqiang Wang University of Virginia, Charlottesville, VA
Available Formats:
Hardcover ISBN: 978-0-8218-9118-6
Product Code: GSM/144
List Price: $68.00 MAA Member Price:$61.20
AMS Member Price: $54.40 Electronic ISBN: 978-0-8218-9447-7 Product Code: GSM/144.E List Price:$64.00
MAA Member Price: $57.60 AMS Member Price:$51.20
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List Price: $102.00 MAA Member Price:$91.80
AMS Member Price: $81.60 Click above image for expanded view Dualities and Representations of Lie Superalgebras Shun-Jen Cheng Academia Sinica, Taipei, Taiwan Weiqiang Wang University of Virginia, Charlottesville, VA Available Formats:  Hardcover ISBN: 978-0-8218-9118-6 Product Code: GSM/144  List Price:$68.00 MAA Member Price: $61.20 AMS Member Price:$54.40
 Electronic ISBN: 978-0-8218-9447-7 Product Code: GSM/144.E
 List Price: $64.00 MAA Member Price:$57.60 AMS Member Price: $51.20 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$102.00 MAA Member Price: $91.80 AMS Member Price:$81.60
• Book Details

Volume: 1442012; 302 pp
MSC: Primary 17;

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.

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. Finite-dimensional 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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Volume: 1442012; 302 pp
MSC: Primary 17;

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.