RTG Combinatorics Seminar: A combinatorial formula for interpolation Macdonald polynomials

Lauren Williams, Harvard University Title: A combinatorial formula for interpolation Macdonald polynomials Abstract: In 1996, Knop and Sahi introduced a remarkable family of inhomogeneous symmetric polynomials called interpolation Macdonald polynomials, which are defined via vanishing conditions. The top homogeneous parts of interpolation Macdonald polynomials are exactly the Macdonald polynomials, themselves a famous family of polynomials which are connected to the Hilbert scheme and knot invariants. The Macdonald polynomials admit several combinatorial formulas, the first being the 2004 tableaux formula of Haglund-Haiman-Loehr. Later, in 2018, Corteel and Mandelshtam and I gave a combinatorial formula for Macdonald polynomials in terms of multiline queues. In very recent work with Houcine Ben Dali, we give the first combinatorial formula for interpolation Macdonald polynomials; our formula is in terms of signed multiline queues, and generalizes the multiline queue formula for Macdonald polynomials. We also give a tableaux formula.