Conference abstracts

Session S10 - Homological Methods

July 28, 16:30 ~ 17:00

## The syzygies of some thickenings of determinantal varieties

### Claudiu Raicu

### University of Notre Dame, USA - craicu@nd.edu

The space of m x n matrices admits a natural action of the group GL_m x GL_n via row and column operations on the matrix entries. The invariant closed subsets are the determinantal varieties defined by the (reduced) ideals of minors of the generic matrix. The minimal free resolutions of these ideals are well-understood by work of Lascoux and others. There are however many more invariant ideals which are non-reduced, and they were classified by De Concini, Eisenbud and Procesi in the 80s. I will explain how to determine the syzygies of a large class of these ideals by employing a surprising connection with the representation theory of general linear Lie superalgebras.

Joint work with Jerzy Weyman (University of Connecticut).