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Drinfeld-Sokolov hierarchies and diagram automorphisms of affine Kac-Moody algebras (1811.10137v2)
Published 26 Nov 2018 in nlin.SI, math-ph, and math.MP
Abstract: For a diagram automorphism of an affine Kac-Moody algebra such that the folded diagram is still an affine Dynkin diagram, we show that the associated Drinfeld-Sokolov hierarchy also admits an induced automorphism. Then we show how to obtain the Drinfeld-Sokolov hierarchy associated to the affine Kac-Moody algebra that corresponds to the folded Dynkin diagram from the invariant sub-hierarchy of the original Drinfeld-Sokolov hierarchy.
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