By Shun-jen Cheng, Weiqiang Wang
This booklet supplies a scientific account of the constitution and illustration concept of finite-dimensional advanced Lie superalgebras of classical variety and serves as an excellent advent to illustration thought of Lie superalgebras. a number of folklore effects are conscientiously proved (and sometimes corrected in detail), occasionally with new proofs. 3 very important dualities are awarded within the e-book, with the unifying subject matter of picking irreducible characters of Lie superalgebras. so as of accelerating sophistication, they're Schur duality, Howe duality, and great duality. The combinatorics of symmetric services is built as wanted in connections to Harish-Chandra homomorphism in addition to irreducible characters for Lie superalgebras. Schur-Sergeev duality for the queer Lie superalgebra is gifted from scratch with whole element. Howe duality for Lie superalgebras is gifted in ebook shape for the 1st time. tremendous duality is a brand new technique constructed long ago few years towards realizing the Bernstein-Gelfand-Gelfand classification of modules for classical Lie superalgebras. tremendous duality relates the illustration thought of classical Lie superalgebras on to the illustration conception of classical Lie algebras and hence offers an answer to the irreducible personality challenge of Lie superalgebras through the Kazhdan-Lusztig polynomials of classical Lie algebras.
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