Geometric Methods in Representation Theory Seminar – Jakub Koncki (IMPAN Warsaw & UNC-CH)

Multiplicative structure of the K-theoretic McKay correspondence for Hilbert schemes of points

Abstract: The Hilbert scheme of points in the complex plane is a classical object of study in algebraic geometry. McKay correspondence provides an isomorphism between its K-theory (or cohomology) and the space of symmetric functions, creating a bridge between geometry and combinatorics. Multiplication by a class in the K-theory induces an endomorphism of the space of symmetric functions. In the cohomological case, compact formulas for such maps were found by Lehn and Sorger. The K-theoretical case was studied by Boissiere using torus equivariant techniques. He proved a formula for multiplication by the class of the tautological bundle and stated a conjecture for the remaining generators of K-theory. In the talk, I will show how torus action simplifies this problem and prove the conjectured formula using restriction to a one-dimensional subtorus.
This is a joint work with M. Zielenkiewicz.

Geometric Methods in Representation Theory Seminar Website