Intersection numbers on ${\overline{\mathcal{M}}}_{g,n}$ and BKP hierarchy

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 Brézin-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.

16 pages, minor corrections, references added

References in corpus (2)

• Generation of Matrix Models by W-operators
• Grothendieck's Dessins d'Enfants in a Web of Dualities. II

Cited by in corpus (1)

• Superintegrability and Kontsevich-Hermitian relation