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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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1610.07534.pdf
(Preprint), 402KB

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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: http://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 $\textit{topological ODE}$.