Quasi-polynomial generalizations of Macdonald polynomials
Vidya Venkateswaran (CCR Princeton)
Tuesday 20th May 16:00-17:00
Maths 311B
Abstract
In joint work with Siddhartha Sahi and Jasper Stokman, we constructed (quasi-)polynomial generalizations of nonsymmetric Macdonald polynomials for arbitrary reduced root systems. We will introduce these objects and discuss how they arise from a family of cyclic Y-parabolically induced DAHA modules where the T_i operators act via "truncated'' divided difference operators. We will also connect a limiting case of these polynomials to metaplectic Whittaker functions, and discuss recent duality results between (anti-)symmetric quasi-polynomials and partially (anti-)symmetric polynomials.
This will be a zoom talk streamed live in the seminar room
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