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Reverse plane partitions and components of quiver Grassmannians
Algebraic Geometry and Number Theory| Speaker: | Joel Kamntitzer, University of Toronto |
| Related Webpage: | http://www.math.toronto.edu/jkamnitz/ |
| Location: | zoom |
| Start time: | Tue, Oct 12 2021, 11:00AM |
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.