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arXiv · 1111.5349

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

A. Alexandrov
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Abstract

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. An important feature of this group element is its simplicity: this is a group element of the Virasoro subalgebra of $gl(\infty)$. 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.

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A. Alexandrov. 2013-09-01. From Hurwitz numbers to Kontsevich-Witten tau-function: a connection by Virasoro operators. https://doi.org/10.1007/s11005-013-0655-0

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