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Integrability of classical affine W-algebras

Published 2 Jul 2020 in math-ph, math.MP, math.RA, math.RT, and nlin.SI | (2007.01244v2)

Abstract: We prove that all classical affine W-algebras W(g,f), where g is a simple Lie algebra and f is its non-zero nilpotent element, admit an integrable hierarchy of bi-Hamiltonian PDEs, except possibly for one nilpotent conjugacy class in G_2, one in F_4, and five in E_8.

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