By Shun-jen Cheng, Weiqiang Wang

This e-book supplies a scientific account of the constitution and illustration thought of finite-dimensional advanced Lie superalgebras of classical kind and serves as a very good 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 vital dualities are provided within the ebook, with the unifying subject matter of picking irreducible characters of Lie superalgebras. so as of accelerating sophistication, they're Schur duality, Howe duality, and tremendous duality. The combinatorics of symmetric capabilities is constructed 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 entire element. Howe duality for Lie superalgebras is gifted in e-book shape for the 1st time. tremendous duality is a brand new strategy built long ago few years towards knowing the Bernstein-Gelfand-Gelfand classification of modules for classical Lie superalgebras. tremendous duality relates the illustration concept of classical Lie superalgebras on to the illustration thought of classical Lie algebras and therefore provides an answer to the irreducible personality challenge of Lie superalgebras through the Kazhdan-Lusztig polynomials of classical Lie algebras.

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Additional resources for Dualities and Representations of Lie Superalgebras (Graduate Studies in Mathematics)

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