Super duality and Kazhdan-Lusztig polynomials
Representation Theory
2008-07-22 v2 High Energy Physics - Theory
Quantum Algebra
Abstract
We establish a direct connection between the representation theories of Lie algebras and Lie superalgebras (of type A) via Fock space reformulations of their Kazhdan-Lusztig theories. As a consequence, the characters of finite-dimensional irreducible modules of the general linear Lie superalgebra are computed by the usual parabolic Kazhdan-Lusztig polynomials of type A. In addition, we establish closed formulas for canonical and dual canonical bases for the tensor product of any two fundamental representations of type A.
Cite
@article{arxiv.math/0409016,
title = {Super duality and Kazhdan-Lusztig polynomials},
author = {Shun-Jen Cheng and Weiqiang Wang and R. B. Zhang},
journal= {arXiv preprint arXiv:math/0409016},
year = {2008}
}
Comments
v.2, substantially revised and streamlined, title modified, 45 pages