2012-02-10

Heisenberg algebras and Hilbert Schemes

Tony Licata, IAS, Princeton

In the mid 90s, Grojnowski and Nakajima constructed representations of affine Lie algebras geometrically using Hilbert schemes of points on the minimal resolution of an ADE simple singularity. This construction gives a fantastic interpretation of the appearance of ADE Dynkin diagrams in both Lie theory and geometry. We will upgrade the Grojnowski-Nakajima one level by describing an action of the affine Lie algebra on the derived categories of Hilbert schemes. (Joint with Sabin Cautis).