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.

中文翻译：

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仿射 Kac-Moody 代数的 Drinfeld-Sokolov 层次结构和图自同构

对于仿射 Kac-Moody 代数的图自同构，使得折叠图仍然是仿射 Dynkin 图，我们表明相关的 Drinfeld-Sokolov 层次结构也承认诱导自同构。然后我们展示了如何从原始 Drinfeld-Sokolov 层次结构的不变子层次结构中获得与对应于折叠 Dynkin 图的仿射 Kac-Moody 代数相关联的 Drinfeld-Sokolov 层次结构。