Givental symmetries of Frobenius manifolds and multi-component KP tau-functions

Evgeny Feigin; Johan van de Leur; Sergey Shadrin

doi:10.1016/j.aim.2009.12.015

Givental symmetries of Frobenius manifolds and multi-component KP tau-functions

Evgeny Feigin^*, Johan van de Leur, Sergey Shadrin

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	1031-1056
Number of pages	26
Journal	Advances in Mathematics
Volume	224
Issue number	3
DOIs	https://doi.org/10.1016/j.aim.2009.12.015
State	Published - Jun 2010
Externally published	Yes

Keywords

Frobenius manifolds
KP tau-functions

Access to Document

10.1016/j.aim.2009.12.015

Cite this

@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",

}

TY - JOUR

T1 - Givental symmetries of Frobenius manifolds and multi-component KP tau-functions

AU - Feigin, Evgeny

AU - van de Leur, Johan

AU - Shadrin, Sergey

N1 - 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.

PY - 2010/6

Y1 - 2010/6

N2 - 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.

AB - 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.

KW - Frobenius manifolds

KW - KP tau-functions

UR - http://www.scopus.com/inward/record.url?scp=77952886542&partnerID=8YFLogxK

U2 - 10.1016/j.aim.2009.12.015

DO - 10.1016/j.aim.2009.12.015

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:77952886542

SN - 0001-8708

VL - 224

SP - 1031

EP - 1056

JO - Advances in Mathematics

JF - Advances in Mathematics

IS - 3

ER -

Givental symmetries of Frobenius manifolds and multi-component KP tau-functions

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this