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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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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-01148689
Contributor : Mattia Cafasso Connect in order to contact the contributor
Submitted on : Tuesday, May 5, 2015 - 9:57:57 AM
Last modification on : Wednesday, October 20, 2021 - 3:18:53 AM

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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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