Dualities for Lie superalgebras

Details Dualities for Lie superalgebras Dualities for Lie superalgebras

2009-12-31

arxiv.org/abs/1001.0074v2

Mathematics

Representation Theory

41 pages, lecture notes for ECNU summer school 2009 in Shanghai, version 2, minor changes, some typos fixed and refenreces add

Scientific paper

We explain how Lie superalgebras of types gl and osp provide a natural framework generalizing the classical Schur and Howe dualities. This exposition includes a discussion of super duality, which connects the parabolic categories O between classical Lie superalgebras and Lie algebras. Super duality provides a conceptual solution to the irreducible character problem for these Lie superalgebras in terms of the classical Kazhdan-Lusztig polynomials.

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