ILW equation for the Hodge integrals revisited

In a previous paper we proved that after a simple transformation the generating series of the linear Hodge integrals on the moduli space of stable curves satisfies the hierarchy of the Intermediate LongWave equation. In this paper we present a much shorter proof of this fact. Our new proof is based on an explicit formula for the one-point linear Hodge integrals that was found independently by Faber, Pandharipande and Ekedahl, Lando, Shapiro, Vainshtein.

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Accepted 22 October 2015

Published 8 July 2016