An Introduction to q-Whittaker Polynomials
Time: 2025-03-07
Published By: He Liu
Speaker(s): Aritra Bhattacharya(BICMR)
Time: 15:00-16:00 March 10, 2025
Venue: Room 77201, Jingchunyuan 78, BICMR
The q-Whittaker polynomials are a remarkable family of symmetric polynomials that arises as specializations of Macdonald polynomials, and generalize the Schur polynomials and elementary symmetric functions. These are related to the Hall-Littlewood polynomials by an application of the classical $\omega$-involution.
The q-Whittaker polynomials show up in a variety of situations. In representation theory of affine Kac-Moody algebras, they are characters of certain level 1 Demazure modules. They encode counting points over a finite field of some (generalized Springer fibers) subvarieties of the flag variety. In addition, they have beautiful combinatorial interpretations involving column strict fillings, partition overlayed GT patterns and semistandard Young tableaux.
In this talk I will try to give an overview of some of these results and some interplay between them.
