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

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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).
To appear in European Journal of Combinatorics

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Representation Theory

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http://salesiana.dossiersoluciones.com/handle/123456789/157280

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0607038
 http://arxiv.org/abs/math/0607038

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arXiv