Schur Q-Polynomials and Kontsevich-Witten Tau Function

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.

45 pages. Improved presentation, and corrected typos

References in corpus (1)

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

Cited by in corpus (2)

• Generalized Brézin-Gross-Witten tau-function as a hypergeometric solution of the BKP hierarchy
• Action of Virasoro operators on Hall-Littlewood polynomials