Infinite-Dimensional Algebra Seminar

Speaker: Tudor Pădurariu (University of Bonn​​​​​​​) Title: Abelian quasi-BPS categories Abstract: I will report on joint work in progress with Sabin Cautis and Yukinobu Toda. The Grothendieck group of the Hall category of a quiver is isomorphic to a positive half of the quantum affine algebra corresponding to the quiver. We show that two structures on the Hall category are compatible: a perverse coherent t-structure and a filtration by window categories. In particular, we construct t-structures on the so-called quasi-BPS categories, which generate Hall categories. We thus obtain a refinement of the total BPS cohomology of the quiver, whose dimension is the value at one of the Kac polynomial of the quiver, in terms of nilpotent orbits. I will discuss examples of quasi-BPS categories for finite-type quivers, where they may be compared with categories of representations of KLR algebras, and for the Jordan quiver. As a corollary, we prove a conjecture of Gorsky–Negut about generators of the category of coherent sheaves on the commuting stack. Zoom: https://mit.zoom.us/j/91800438944. For the Passcode, please contact Pavel Etingof at [email protected]. Note: the seminar will run on occasion throughout this Fall semester.