Deformed Kazhdan-Lusztig elements and Macdonald polynomials

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We introduce deformations of Kazhdan-Lusztig elements and specialised non-symmetric 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. © 2011.




De Gier, J., Lascoux, A., & Sorrell, M. (2012). Deformed Kazhdan-Lusztig elements and Macdonald polynomials. Journal of Combinatorial Theory. Series A, 119(1), 183–211.

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