Enumerative geometry, tau-functions and Heisenberg-Virasoro algebra
arXiv:1404.3402 · doi:10.1007/s00220-015-2379-8
Abstract
In this paper we establish relations between three enumerative geometry tau-functions, namely the Kontsevich-Witten, Hurwitz and Hodge tau-functions. The relations allow us to describe the tau-functions in terms of matrix integrals, Virasoro constraints and Kac-Schwarz operators. All constructed operators belong to the algebra (or group) of symmetries of the KP hierarchy.
65 pages; minor corrections