A representation of the spherical double affine Hecke algebra on the quantum cohomology ring of a Grassmannian

Vincent Gajda (University of Bonn)

Wednesday 26th September 16:00-17:00 Maths 311B

Abstract

First we discuss some basic concepts involving the double affine Hecke algebra associated to GL_n. In particular, we will define the spherical DAHA, which is an idempotent truncation of the DAHA. Under the assumption that the parameters of the DAHA are primitive N-th roots of unity for N>n we will construct a representation of the spherical DAHA on the quantum cohomology ring (specialized at q=1) of the Grassmannian of n-planes in an N-dimensional complex vector space.

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