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Vanishing integrals for Hall-Littlewood polynomials
Algebra & Discrete Mathematics| Speaker: | Vidya Venkateswaran, Cal Tech |
| Location: | 2112 MSB |
| Start time: | Fri, Dec 2 2011, 2:10PM |
Description
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.