Algebraic Combinatorics Seminar - Victor Reiner

Title: Sandpiles and representation theory

Abstract:

For an undirected graph, its sandpile group is an interesting isomorphism invariant-- it is a finite abelian group that describes the integer cokernel of the graph's Laplacian matrix. This talk will discuss joint work with G. Benkart and C. Klivans examining an analogous invariant for a complex representation of a finite group, built from what one might call its "McKay matrix".  We will then discuss work with D. Grinberg and J. Huang which generalizes this to modules over finite-dimensional Hopf algebras.