This article is cited in 9 papers

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

Marco Bertola^abc, Boris Dubrovin^ad, Di Yang<sup>ef

a</sup> SISSA, via Bonomea 265, Trieste 34136, Italy
^b Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve W., Montréal, Québec, H3G 1M8, Canada
^c Centre de recherches mathématiques, Université de Montréal, C. P. 6128, succ. centre ville, Montréal, Québec, H3C 3J7, Canada
^d N. N. Bogolyubov Laboratory for Geometrical Methods in Mathematical Physics, Moscow State University, Moscow 119899, Russia

^e Max-Planck-Institut für Mathematik, Vivatsgasse 7, Bonn 53111, Germany
^f School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, P.R. China

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 topological ODE.

Key words and phrases: simple Lie algebra, tau-function, Drinfeld–Sokolov hierarchy, matrix resolvent, topological ODE.

MSC: Primary 37K10; Secondary 53D45, 17B80, 14N35

Language: English

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

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