Dualities and Representations of Lie Superalgebras is popular PDF and ePub book, written by Shun-Jen Cheng in 2012, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Dualities and Representations of Lie Superalgebras can be Read Online from any device for your convenience.
Dualities and Representations of Lie Superalgebras Book PDF Summary
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.
Detail Book of Dualities and Representations of Lie Superalgebras PDF
- Author : Shun-Jen Cheng
- Release : 01 October 2024
- Publisher : American Mathematical Soc.
- ISBN : 9780821891186
- Genre : Mathematics
- Total Page : 323 pages
- Language : English
- PDF File Size : 7,7 Mb
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