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

Bertola, Marco; Dubrovin, Boris; Yang, Di

doi:10.17323/1609-4514-2021-21-2-233-270

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

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Yang, Di
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.17323/1609-4514-2021-21-2-233-270
(Publisher version)

https://doi.org/10.48550/arXiv.1610.07534
(Preprint)

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Citation

Bertola, M., Dubrovin, B., & Yang, D. (2021). Simple Lie algebras, Drinfeld-Sokolov hierarchies, and multi-point correlation functions. Moscow Mathematical Journal, 21(2), 233-270. doi:10.17323/1609-4514-2021-21-2-233-270.

Cite as: https://hdl.handle.net/21.11116/0000-0008-B236-2

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 $\textit{topological ODE}$.