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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 $\textit{topological ODE}$.