Seminars & Colloquia Calendar

Download as iCal file

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.

Zoom link
Meeting ID: 939 2146 5287
Passcode: 196884

Special Note to All Travelers

Directions: map and driving directions. If you need information on public transportation, you may want to check the New Jersey Transit page.

Unfortunately, cancellations do occur from time to time. Feel free to call our department: 848-445-6969 before embarking on your journey. Thank you.