Borodin-Okounkov formula, string equation and topological solutions of Drinfeld-Sokolov hierarchies

Abstract : We give a general method to compute the expansion of topological tau functions for Drinfeld-Sokolov hierarchies associated to an arbitrary untwisted affine Kac-Moody algebra. Our method consists of two main steps: first these tau functions are expressed as (formal) Fredholm determinants of the type appearing in the Borodin-Okounkov formula, then the kernels for these determinants are found using a reduced form of the string equation. A number of explicit examples are given.
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Pré-publication, Document de travail
2015
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https://hal.archives-ouvertes.fr/hal-01148689
Contributeur : Mattia Cafasso <>
Soumis le : mardi 5 mai 2015 - 09:57:57
Dernière modification le : lundi 5 février 2018 - 15:00:03

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  • HAL Id : hal-01148689, version 1
  • ARXIV : 1505.00556

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Mattia Cafasso, Chao-Zhong Wu. Borodin-Okounkov formula, string equation and topological solutions of Drinfeld-Sokolov hierarchies. 2015. 〈hal-01148689〉

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