@article {2004,
title = {Virasoro Symmetries of the Extended Toda Hierarchy},
journal = {Comm. Math.\\nPhys. 250 (2004) 161-193.},
number = {arXiv.org;math/0308152},
year = {2004},
abstract = {We prove that the extended Toda hierarchy of \\\\cite{CDZ} admits nonabelian Lie algebra of infinitesimal symmetries isomorphic to the half of the Virasoro algebra. The generators $L_m$, $m\\\\geq -1$ of the Lie algebra act by linear differential operators onto the tau function of the hierarchy. We also prove that the tau function of a generic solution to the extended Toda hierarchy is annihilated by a combination of the Virasoro operators and the flows of the hierarchy. As an application we show that the validity of the Virasoro constraints for the $CP^1$ Gromov-Witten invariants and their descendents implies that their generating function is the logarithm of a particular tau function of the extended Toda hierarchy.},
doi = {10.1007/s00220-004-1084-9},
url = {http://hdl.handle.net/1963/2544},
author = {Boris Dubrovin and Zhang Youjin}
}