Intersection numbers on $\overline {\mathcal M}_{g,n}$ and BKP hierarchy
Mathematical Physics
2021-01-18 v3 High Energy Physics - Theory
Algebraic Geometry
math.MP
Exactly Solvable and Integrable Systems
Abstract
In their recent inspiring paper Mironov and Morozov claim a surprisingly simple expansion formula for the Kontsevich-Witten tau-function in terms of the Schur Q-functions. Here we provide a similar conjecture for the Br\'ezin-Gross-Witten tau-function. Moreover, we identify both tau-functions of the KdV hierarchy, which describe intersection numbers on the moduli spaces of punctured Riemann surfaces, with the hypergeometric solutions of the BKP hierarchy.
Cite
@article{arxiv.2012.07573,
title = {Intersection numbers on $\overline {\mathcal M}_{g,n}$ and BKP hierarchy},
author = {Alexander Alexandrov},
journal= {arXiv preprint arXiv:2012.07573},
year = {2021}
}
Comments
16 pages, minor corrections, references added