Representation Theory and Mathematical Physics Seminar: Dyck path algebra and Hilbert schemes

Seminar | September 19 | 3-4 p.m. | 891 Evans Hall

 Eugene Gorsky, UC Davis

 Department of Mathematics

Carlsson and Mellit introduced the Dyck path algebra and its polynomial representation, which was used to prove some important conjectures in algebraic combinatorics. I will define this algebra and construct its action on the equivariant K-theory of certain smooth strata in the flag Hilbert schemes of points on the plane. In this presentation, the fixed points of torus action correspond to generalized Macdonald polynomials and the the matrix elements of the operators have explicit combinatorial presentation. The talk is based on a joint work with Erik Carlsson and Anton Mellit.