Algebra and Geometry Seminar

It has been shown that a category O associated with the affine Grassmannian is equivalent to the category of modules for a decorated KLR algebra. The affine Grassmannian gives rise to a perfect basis called the Mirkovic-Vilonen basis, while the KLR algebra gives rise to a perfect basis called Lusztig's canonical basis. In previous work I used equivariant volumes to compare such bases. This talk will explain a relevant notion of volume for well-behaved module categories such as KLR-mod, and how it is used (in joint work in progress, with Alexis Leroux-Lapierre) to study the MV-KLR change of basis.