Drinfeld-Sokolov hierarchies and diagram automorphisms of affine Kac-Moody algebras
arXiv:1811.10137 · doi:10.1007/s00220-019-03568-4
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.
48 pages