
Preface  Preview Material  Table of Contents  Index  Supplementary Material 
Graduate Studies in Mathematics 2012; 302 pp; hardcover Volume: 144 ISBN10: 0821891189 ISBN13: 9780821891186 List Price: US$64 Member Price: US$51.20 Order Code: GSM/144 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 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. Readership Graduate students and research mathematicians interested in Lie algebras, Lie superalgebras, representation theory, mathematical physics, and especially supersymmetry. 


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