Tau Functions and the Limit of Block Toeplitz Determinants


Autoria(s): Cafasso, Mattia; Wu, Chao-Zhong
Contribuinte(s)

Laboratoire Angevin de REcherche en MAthématiques (LAREMA) ; Centre National de la Recherche Scientifique (CNRS) - Université d'Angers (UA)

Data(s)

2015

Resumo

International audience

<p>A classical way to introduce tau functions for integrable hierarchies of solitonic equations is by means of the Sato–Segal–Wilson infinite-dimensional Grassmannian. Every point in the Grassmannian is naturally related to a Riemann–Hilbert problem on the unit circle, for which Bertola proposed a tau function that generalizes the Jimbo–Miwa–Ueno tau function for isomonodromic deformation problems. In this paper, we prove that the Sato–Segal–Wilson tau function and the (generalized) Jimbo–Miwa–Ueno iso- monodromic tau function coincide under a very general setting, by identifying each of them to the large-size limit of a block Toeplitz determinant. As an application, we give a new definition of tau function for Drinfeld–Sokolov hierarchies (and their generalizations) by means of infinite-dimensional Grassmannians, and clarify their relation with other tau functions given in the literature.</p>

Identificador

hal-01392114

https://hal.archives-ouvertes.fr/hal-01392114

DOI : 10.1093/imrn/rnu262

OKINA : ua12559

Idioma(s)

en

Publicador

HAL CCSD

Oxford University Press (OUP)

Relação

info:eu-repo/semantics/altIdentifier/doi/10.1093/imrn/rnu262

Fonte

ISSN: 1073-7928

EISSN: 1687-0247

International Mathematics Research Notices

https://hal.archives-ouvertes.fr/hal-01392114

International Mathematics Research Notices, Oxford University Press (OUP), 2015, 2015 (20), pp.10339-10366. <http://imrn.oxfordjournals.org/content/2015/20/10339>. <10.1093/imrn/rnu262>

http://imrn.oxfordjournals.org/content/2015/20/10339

Palavras-Chave #[MATH] Mathematics [math]
Tipo

info:eu-repo/semantics/article

Journal articles