2005/01/21 by Milanov, Todor E.
#Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.math/0501336
The Extended Toda Hierarchy (shortly ETH) was introduce by E. Getzler \citeGe and independently by Y. Zhang \citeZ in order to describe an integrable hierarchy which governs the Gromov--Witten invariants of \C P1. The \em Lax type presentation of the ETH was given in \citeCDZ. In this paper we give a description of the ETH in terms of \em tau-functions and Hirota Quadratic Equations (known also as Hirota Bilinear Equations). A new feature here is that the Hirota equations are given in terms of vertex operators taking values in the algebra of differential operators on the affine line.