Verlinde/Grassmannian Correspondence

Abstract: In the 90s', Witten gave a physical derivation of an isomorphism between the Verlinde algebra of $\mathrm{GL}(n)$ of level l and the quantum cohomology ring of the Grassmannian $\mathrm{Gr}(n,n+l)$. In the joint work arXiv:1811.01377 with Yongbin Ruan, we proposed a $K$-theoretic generalization of Witten's work by relating the $\mathrm{GL}_n$ Verlinde numbers to the level $l$ quantum $K$-invariants of the Grassmannian $\mathrm{Gr}(n,n+l)$, and refer to it as the Verlinde/Grassmannian correspondence. The correspondence was formulated precisely in the aforementioned paper, and we proved the rank 2 case ($n$=2) there.

In this talk, I will first explain the background of this correspondence and its interpretation in physics. Then I will discuss the main idea of the proof for arbitrary rank. A new technical ingredient is the virtual nonabelian localization formula developed by Daniel Halpern-Leistner.

algebraic geometry

Audience: researchers in the topic

UBC Vancouver Algebraic Geometry Seminar

Series comments: Recordings and slides are available on the seminar webpage:

wiki.math.ubc.ca/mathbook/alggeom-seminar/Main_Page