Lie Groups Seminar

Siddhartha SahiRutgers University
Quasi-polynomial representations of double affine Hecke algebras and a generalization of Macdonald polynomials

Friday, September 3, 2021 - 3:45pm
Malott 406

Macdonald polynomials are a remarkable family of functions.
They are a common generalization of many different families of
special functions arising in the representation theory of reductive
groups, including spherical functions and Whittaker functions.

In turn, Macdonald polynomials can be understood in terms of
a certain representation of Cherednik's double affine Hecke
algebra (DAHA), acting on polynomial functions on a torus.

Whittaker functions admit a natural generalization to the setting
of metaplectic covers of reductive p-adic groups, which play a
key role in the theory of Weyl group multiple Dirichlet series.

It turns out that Macdonald polynomials also admit a corresponding
generalization, which can be understood in terms of a representation
of the DAHA on the space of quasi-polynomial functions on a torus.

This is joint work with Jasper Stokman and Vidya Venkateswaran.