%0 Journal Article
%J Comm. Math.\\nPhys. 250 (2004) 161-193.
%D 2004
%T Virasoro Symmetries of the Extended Toda Hierarchy
%A Boris Dubrovin
%A Zhang Youjin
%X 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.
%B Comm. Math.\\nPhys. 250 (2004) 161-193.
%G en_US
%U http://hdl.handle.net/1963/2544
%1 1575
%2 Mathematics
%3 Mathematical Physics
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-12-21T12:53:52Z\\nNo. of bitstreams: 1\\n0308152v2.pdf: 341202 bytes, checksum: 306b1f696e6ec01c0eabbeeeca895290 (MD5)
%R 10.1007/s00220-004-1084-9