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A combinatorial formula for interpolation Macdonald polynomials

Presenter
November 13, 2025
Abstract
In 1996, Knop and Sahi introduced a remarkable family of inhomogeneous symmetric polynomials, defined via vanishing conditions, whose top homogeneous parts are exactly the Macdonald polynomials. Like the Macdonald polynomials, these inter-polation Macdonald polynomials are closely connected to the Hecke algebra, and admit nonsymmetric versions, which generalize the nonsymmetric Macdonald polynomials. In this talk I will explain joint work with Houcine Ben Dali in which we give a combinatorial formula for interpolation Macdonald polynomials in terms of signed multiline queues; this formula generalizes the combinatorial formula for Macdonald polynomials in terms of multiline queues given by Corteel–Mandelshtam-W. We also have a tableaux formula for these polynomials.