The fundamental local equivalence via special functions

Valentin Buciumas

Tuesday 21st January 16:00-17:00 Maths 311B

Abstract

My talk will focus on an interesting class of special functions that are symmetric with respect to some twisted action of the symmetric group (called the Chinta-Gunnells action). These functions can be used to model a graded version of the representation theory of Lusztig's quantum group at a root of unity, as well as certain Whittaker spaces on p-adic groups (the fact that the quantum and p-adic settings are equivalent is what is known as the fundamental local equivalence in geometric Langlands). Moreover, certain structure coefficients for these functions have integral positivity properties; they can be seen to be equal to the transition coefficients from LLT polynomials to Schur polynomials.
In my talk, I will introduce these functions and at the end present some combinatorial results about them that can be attained using solvable lattice models.

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