Super duality and Kazhdan-Lusztig polynomials

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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.
v.2, substantially revised and streamlined, title modified, 45 pages

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Representation Theory, High Energy Physics - Theory, Quantum Algebra

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http://salesiana.dossiersoluciones.com/handle/123456789/165413

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0409016
 http://arxiv.org/abs/math/0409016
 Trans. AMS 360 (2008), 5883--5924.

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arXiv