Dualities for Lie superalgebras
Representation Theory
2012-07-09 v2 Quantum Algebra
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.
Cite
@article{arxiv.1001.0074,
title = {Dualities for Lie superalgebras},
author = {Shun-Jen Cheng and Weiqiang Wang},
journal= {arXiv preprint arXiv:1001.0074},
year = {2012}
}
Comments
41 pages, lecture notes for ECNU summer school 2009 in Shanghai, version 2, minor changes, some typos fixed and refenreces added/updated.