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arXiv · 1505.00556

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

Mattia Cafasso·Chao-Zhong Wu
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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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Mattia Cafasso, Chao-Zhong Wu. 2019-11-12. Borodin-Okounkov formula, string equation and topological solutions of Drinfeld-Sokolov hierarchies. https://doi.org/10.1007/s11005-019-01205-8

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