Kontsevich-Witten and Brezin-Gross-Witten Tau-functions as Schur Q-polynomials
Time: 2021-04-12
Published By: He Liu
Speaker(s): Chenglang Yang (Peking University)
Time: 16:00-17:00 April 13, 2021
Venue: Room 29, Quan Zhai, BICMR
In this talk, I will introduce our recent works on expressing the Kontsevich-Witten and Brezin-Gross-Witten tau-functions as linear combinations of Schur Q-polynomials. These expressions are conjectured by Mironov -Morozov and Alexandrov respectively.
The KW and BGW tau-functions are generating functions for intersection numbers on the moduli spaces of stable curves. Both of them are tau-functions of KdV hierarchy and have matrix models' descriptions in physics, which are related to the 2D topological gravity and lattice gauge theory respectively. The Schur Q-polynomials are related to the projective representations of symmetric groups, and are polynomial tau-functions of BKP hierarchy. In this talk, I will review them, and talk about our proofs of above conjectures. The talk is based on joint works with Xiaobo Liu.
