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arXiv · 1610.07534

Simple Lie algebras, Drinfeld--Sokolov hierarchies, and multi-point correlation functions

Marco Bertola·Boris Dubrovin·Di Yang
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Abstract

For a simple Lie algebra $\mathfrak{g}$, we derive a simple algorithm for computing logarithmic derivatives of tau-functions of Drinfeld--Sokolov hierarchy of $\mathfrak{g}$-type in terms of $\mathfrak{g}$-valued resolvents. We show, for the topological solution to the lowest-weight-gauge Drinfeld--Sokolov hierarchy of $\mathfrak{g}$-type, the resolvents evaluated at zero satisfy the $\textit{topological ODE}$.

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Marco Bertola, Boris Dubrovin, Di Yang. 2016-10-24. Simple Lie algebras, Drinfeld--Sokolov hierarchies, and multi-point correlation functions. https://arxiv.org/abs/1610.07534

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