Geometric operators on the equivariant K-theory of the space of partial flags.Algebra & Discrete Mathematics
|Mikhail Mazin, Kansas State University
|Fri, Feb 10 2017, 2:10PM
In this talk, I will discuss recent developments in a project relating geometry, representation theory and combinatorics. The goal of this project is to construct a geometric action of the 0-degenerate affine Schur algebra on the equivariant K-theory of the space of partial flags. However, such an algebra has not been defined yet, so its definition should transpire as a result of this project. We consider the equivariant K-theory of the space of partial flags, construct certain geometric operators acting on it, and compute relations between them. Combinatorially, this corresponds to certain explicit operators between different spaces of partially symmetric polynomials in d variables.
This is a work in progress, joint with Sergey Arkhipov.