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Parabolic Kazhdan-Lusztig polynomials, plethysm and gereralized Hall-Littlewood functions for classical types

Cedric Lecouvey
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Abstract

We use power sums plethysm operators to introduce H functions which interpolate between the Weyl characters and the Hall-Littlewood functions Q' corresponding to classical Lie groups. The coefficients of these functions on the basis of Weyl characters are parabolic Kazhdan-Lusztig polynomials and thus, are nonnegative. We prove that they can be regarded as quantizations of branching coefficients obtained by restriction to certain Levi subgroups. The H functions associated to linear groups coincide with the polynomials introduced by Lascoux Leclerc and Thibon (LLT polynomials).

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BibTeXRIS

Cedric Lecouvey. 2008-03-24. Parabolic Kazhdan-Lusztig polynomials, plethysm and gereralized Hall-Littlewood functions for classical types. https://arxiv.org/abs/math/0607038

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