Vanishing integrals for Hall-Littlewood polynomialsAlgebra & Discrete Mathematics
|Vidya Venkateswaran, Cal Tech
|Fri, Dec 2 2011, 2:10PM
In a recent paper, Rains and Vazirani used Hecke algebra techniques to develop (q,t)-generalizations of a number of well-known vanishing identities for Schur functions. However, their approach does not work directly at q=0 (the Hall-Littlewood level). We discuss a technique that is more combinatorial in nature, and allows us to obtain generalizations of some of their results at q=0 as well as a finite-dimensional analog of a recent summation formula of Warnaar. We will also briefly explain how these results are related to p-adic representation theory. Finally, we will explain how this method can be extended to give an explicit construction of Hall-Littlewood polynomials of type BC.