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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.

Dates and versions

hal-01148689 , version 1 (05-05-2015)

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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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