Deformed Kazhdan-Lusztig elements and Macdonald polynomials

Details Deformed Kazhdan-Lusztig elements and Macdonald polynomials Deformed Kazhdan-Lusztig elements and Macdonald polynomials

2010-07-06

arxiv.org/abs/1007.0861v2

J. Alg. Comb. Theory A 119 (2012), 183-211

Mathematics

Combinatorics

major revision, 29 pages, 22 eps figures

Scientific paper

We introduce deformations of Kazhdan-Lusztig elements and specialised nonsymmetric Macdonald polynomials, both of which form a distinguished basis of the polynomial representation of a maximal parabolic subalgebra of the Hecke algebra. We give explicit integral formula for these polynomials, and explicitly describe the transition matrices between classes of polynomials. We further develop a combinatorial interpretation of homogeneous evaluations using an expansion in terms of Schubert polynomials in the deformation parameters.

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