Reverse plane partitions and components of quiver Grassmannians

Abstract: A classic result in geometric representation theory relates components of Springer fibres to semistandard Young tableaux. I will explain how to generalize this result to reverse plane partitions. These RPPs are decreasing functions on a minuscule heap and they provide a combinatorial model for the crystal of the coordinate ring of a minuscule flag variety. Associated to the minuscule heap, we define a module for a preprojective algebra. The space of submodule of this module (called a quiver Grassmannian) is isomorphic to the core of a Nakajima quiver variety. Our main result is that these RPPs are in bijection with the irreducible components of this quiver Grassmannian.

algebraic geometry

Audience: researchers in the topic

UC Davis algebraic geometry seminar