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Dualities and Representations of Lie Superalgebras
Shun-Jen Cheng, Academia Sinica, Taipei, Taiwan, and Weiqiang Wang, University of Virginia, Charlottesville, VA
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Graduate Studies in Mathematics
2012; 302 pp; hardcover
Volume: 144
ISBN-10: 0-8218-9118-9
ISBN-13: 978-0-8218-9118-6
List Price: US$64
Member Price: US$51.20
Order Code: GSM/144
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See also:

Enveloping Algebras - Jacques Dixmier

Lie Superalgebras and Enveloping Algebras - Ian M Musson

Finite Dimensional Algebras and Quantum Groups - Bangming Deng, Jie Du, Brian Parshall and Jianpan 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.

Readership

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

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