Connecting the Kontsevich-Witten and Hodge tau-functions by the $\widehat{GL(\infty )}$ operators

Abstract

In this paper, we present an explicit formula that connects the Kontsevich-Witten tau-function and the Hodge tau-function by differential operators belonging to the $\widehat{GL(\infty )}$ group. Indeed, we show that the two tau-functions can be connected using Virasoro operators. This proves a conjecture posted by Alexandrov in [1].

48 pages

References in corpus (2)

• Efficient computation of the Zassenhaus formula
• Enumerative geometry, tau-functions and Heisenberg-Virasoro algebra

Cited by in corpus (4)

• KP integrability of triple Hodge integrals. II. Generalized Kontsevich matrix model
• Virasoro constraints and polynomial recursion for the linear Hodge integrals
• KP integrability of triple Hodge integrals. III. Cut-and-join description, KdV reduction, and topological recursions
• From Kontsevich-Witten to linear Hodge integrals via Virasoro operators