@article{c7d2de5b447b4c74b4498393a548b31a,

title = "Givental symmetries of Frobenius manifolds and multi-component KP tau-functions",

abstract = "We establish a link between two different constructions of the action of the twisted loop group on the space of Frobenius structures. The first construction (due to Givental) describes the action of the twisted loop group on the partition functions of formal (axiomatic) Gromov-Witten theories. The explicit formulas for the corresponding tangent action were computed by Y.-P. Lee. The second construction (due to van de Leur) describes the action of the same group on the space of Frobenius structures via the multi-component KP hierarchies. Our main theorem states that the genus zero restriction of the Y.-P. Lee formulas coincides with the tangent van de Leur action.",

keywords = "Frobenius manifolds, KP tau-functions",

author = "Evgeny Feigin and {van de Leur}, Johan and Sergey Shadrin",

note = "Funding Information: The work of E.F. was partially supported by the Russian President Grant MK-281.2009.1, by the RFBR grants 09-01-00058, 07-02-00799, and NSh-3472.2008.2, by Pierre Deligne fund based on his 2004 Balzan prize in mathematics and by Alexander von Humboldt Fellowship. The work of J.v.d.L. was partially supported by the European Science Foundation Program MISGAM and the Marie Curie RTN ENIGMA. The work of S.S. was partially supported by the Vidi grant of NWO.",

year = "2010",

month = jun,

doi = "10.1016/j.aim.2009.12.015",

language = "אנגלית",

volume = "224",

pages = "1031--1056",

journal = "Advances in Mathematics",

issn = "0001-8708",

publisher = "Academic Press Inc.",

number = "3",

}