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

2016/10/24 by Bertola, Marco, Dubrovin, Boris, Yang, Di · 2 citations
#Algebraic Geometry (math.AG) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1610.07534

Abstract

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

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