Department of Mathematics - PhD Student Seminar - Geometric construction of Shuffle Algebra acting on Moduli Spaces of Stable Sheaves on Surfaces

Geometric representation theory contains various realizations of representation some infinite dimensional Lie algebras  in geometric ways. In this talk we will introduce a geometric construction of representation of Hecke algebra realizing as action on K-theory groups of moduli spaces of stable bundles on smooth surfaces given by Andrei Negut, which is a generalization of Nakajima’s results on Hilbert scheme of n points on affine plane. In his work, Negut introduces a way to understand the operators on K-theory groups without using equivariant settings.