# Seminars & Colloquia Calendar

Lie Group Quantum Mathematics Seminar

## Combinatorial formula for SSV polynomials

#### Jason Saied, Rutgers University

Location:  Zoom
Date & time: Friday, 26 March 2021 at 12:00PM - 1:00PM

Abstract Macdonald polynomials are homogeneous polynomials that generalize many important representation-theoretic families of polynomials, such as Jack polynomials, Hall-Littlewood polynomials, affine Demazure characters, and Whittaker functions of GL_r(F) (where F is a non-Archimedean field). They may be constructed using the basic representation of the corresponding double affine Hecke algebra (DAHA): a particular commutative subalgebra of the DAHA acts semisimply on the space of polynomials, and the (nonsymmetric) Macdonald polynomials are the simultaneous eigenfunctions. In 2018, Sahi, Stokman, and Venkateswaran constructed a generalization of this DAHA action, recovering the metaplectic Weyl group action of Chinta and Gunnells. As a consequence, they discovered a new family of polynomials, called SSV polynomials, that generalize both Macdonald polynomials and Whittaker functions of metaplectic covers of GL_r(F). We will give a combinatorial formula for these SSV polynomials in terms of alcove walks, generalizing Ram and Yip's formula for Macdonald polynomials.