Virasoro Symmetries of the Extended Toda Hierarchy
Dubrovin, Boris ; Zhang, Youjin
arXiv, 0308152 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2003-08-15
Classification:  Mathematics - Differential Geometry,  Mathematical Physics 
@article{0308152,
     author = {Dubrovin, Boris and Zhang, Youjin},
     title = {Virasoro Symmetries of the Extended Toda Hierarchy},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0308152}
}

Dubrovin, Boris; Zhang, Youjin. Virasoro Symmetries of the Extended Toda Hierarchy. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0308152/