Jan de Gier: Deformed Kazhdan-Lusztig elements and Macdonald polynomials

Abstract

In this talk I will 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. I will show explicit integral formula for these polynomials, and explicitly describe the transition matrices between classes of polynomials. These polynomials are related to alternating sign matrices and the Razumov-Stroganov conjecture. If time permits, I will discuss a combinatorial interpretation of homogeneous evaluations using an expansion in terms of Schubert polynomials in the deformation parameters.