Using Lie Theory to Construct Interesting Tensors

One way to obtain spaces of matrices with generically nonmaximal rank comes from choosing "intermediate" maps arising in objects known as minimal free resolutions. This means that resolutions that are equivariant with respect to a large symmetry group will induce tensors invariant under a large symmetry group, which begs the question: is there a canonical source of large families of equivariant resolutions? In this talk, I'll propose one such source, which arises in the context of Lie theory. This family will at least induce all possible Young flattenings, realizing these tensors as arising from homogeneous pieces of a well-known family of complexes constructed by Eisenbud--Floystad--Weyman. The goal of this talk is to introduce the basic theory tying all of these objects together, the foundation of which is given by an old theorem of Kostant.

This seminar is part of the Problems in Algebraic Geometry Coming from Complexity Theory series.