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

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

2006-07-03

arxiv.org/abs/math/0607038v2

Mathematics

Representation Theory

To appear in European Journal of Combinatorics

Scientific paper

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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