|Speaker:||Anna Puskás (Kavli IPMU)|
|Title:||Demazure-Lusztig operators, Whittaker functions and crystals|
|Date (JST):||Thu, Nov 08, 2018, 15:30 - 17:00|
|Place:||Seminar Room A|
The Casselman-Shalika formula is an explicit formula for values of a spherical Whittaker function over a local nonarchimedean field, in terms of a character of a reductive group. Analogues exist for metaplectic groups that construct a Whittaker function either by averaging over a Weyl group, or by taking a sum over a combinatorial structure such as a highest-weight crystal.
In this talk we will discuss how Demazure Lusztig operators emerged to understand the relationship between the two constructions. They turn out to be useful in the study $p$-adic (Iwahori)-Whittaker functions in both the classical and the metaplectic, finite dimensional and general Kac-Moody setting. In particular, they provide a tool to extend these constructions to a greater generality. In addition, Weyl symmetrizers
built from these operators raise interesting questions related to Macdonald's constant term conjecture.