Branes and DAHA Representations
Organizers
Speaker
Satoshi Nawata
Time
Friday, May 16, 2025 1:00 PM - 2:30 PM
Venue
A3-4-301
Online
Zoom 242 742 6089
(BIMSA)
Abstract
In this talk, I will present a derived equivalence between the A-brane category of a character variety and the representation category of the double affine Hecke algebra (DAHA). Brane quantization, which combines deformation and geometric quantization, is a framework that applies symplectic geometry of a certain character variety to the representation theory of the spherical DAHA. Focusing on the DAHA of $C^\vee C_1$, I will provide solid evidence supporting this derived equivalence. Moreover, this brane quantization approach naturally leads to an affine braid group action on the category as a group of auto-equivalences. As a by-product, our geometric investigation offers detailed information about the low-energy effective dynamics of the SU(2) Nf=4 Seiberg-Witten theory. This talk is based on arXiv:2412.19647 (joint work with Huang, Zhang, and Zhuang) and arXiv:2206.03565 (joint work with Gukov, Koroteev, Pei, and Saberi).