Dualities for Lie superalgebras
arXiv:1001.0074
Abstract
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.
41 pages, lecture notes for ECNU summer school 2009 in Shanghai, version 2, minor changes, some typos fixed and refenreces added/updated.
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