1111.5349 (A. Alexandrov)

From Hurwitz numbers to Kontsevich-Witten tau-function: a connection by
Virasoro operators    [PDF]

A. Alexandrov

In this letter we present our conjecture on the connection between the Kontsevich-Witten and the Hurwitz tau-functions. The conjectural formula connects these two tau-functions by means of the $GL(\infty)$ group element. The important feature of this group element is its simplicity: it is built of only generators of the Virasoro algebra. If proved, this conjecture would allow to derive the Virasoro constraints for the Hurwitz tau-function, which remain unknown in spite of existence of several matrix model representations, as well as to give an integrable operator description of the Kontsevich-Witten tau-function.

View original: http://arxiv.org/abs/1111.5349