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

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• Polynomial averages in the Kontsevich model
• A new cohomology class on the moduli space of curves
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Cited by in corpus (9)

• New Insights into Superintegrability from Unitary Matrix Models
• KdV solves BKP
• Generalized Q-functions for GKM
• Generalized Brézin-Gross-Witten tau-function as a hypergeometric solution of the BKP hierarchy
• Schur Q-Polynomials and Kontsevich-Witten Tau Function
• Superintegrability and Kontsevich-Hermitian relation
• Notes about KP/BKP correspondence
• Action of Virasoro operators on Hall-Littlewood polynomials
• Combinatorics of KP hierarchy structural constants