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.
General
| Imprint: |
American Mathematical Society
|
| Country of origin: |
United States |
| Series: |
Graduate Studies in Mathematics |
| Release date: |
2013 |
| Authors: |
Shun-Jen Cheng
• Weiqiang Wang
|
| Dimensions: |
254 x 178mm (L x W) |
| Format: |
Hardcover
|
| Pages: |
302 |
| ISBN-13: |
978-0-8218-9118-6 |
| Categories: |
Books
Promotions
|
| LSN: |
0-8218-9118-9 |
| Barcode: |
9780821891186 |
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