Abstract:

Using matrix model, Mironov and Morozov recently gave a formula which represents Kontsevich-Witten tau-function as a linear expansion of Schur Q-polynomials. In this paper, we will show directly that the Q-polynomial expansion in this formula satisfies the Virasoro constraints, and consequently obtain a proof of this formula without using matrix model. We also give a proof for Alexandrov's conjecture that Kontsevich-Witten tau-function is a hypergeometric tau-function of the BKP hierarchy after re-scaling.

(Link: https://arxiv.org/abs/2103.14318) 

 

Papers Published: 

[1] X.Liu and C. Yang. Schur Q-Polynomials and Kontsevich-Witten Tau Function, https://arxiv.org/abs/2103.14318

[2] X.Liu and C. Yang. Q-Polynomial expansion for Brezin-Gross-Witten tau-function, https://arxiv.org/abs/2104.01357

 

 

 

 

 

 

 

 

 

        Prof. Liu Xiaobo