Classical Affine W -Algebras and the Associated Integrable Hamiltonian Hierarchies for Classical Lie Algebras
Author(s)De Sole, Alberto; Kac, Victor; Valeri, Daniele
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We prove that any classical affine W-algebra W (g, f) , where g is a classical Lie algebra and f is an arbitrary nilpotent element of g, carries an integrable Hamiltonian hierarchy of Lax type equations. This is based on the theories of generalized Adler type operators and of generalized quasideterminants, which we develop in the paper. Moreover, we show that under certain conditions, the product of two generalized Adler type operators is a Lax type operator. We use this fact to construct a large number of integrable Hamiltonian systems, recovering, as a special case, all KdV type hierarchies constructed by Drinfeld and Sokolov.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Communications in Mathematical Physics
Springer Berlin Heidelberg
De Sole, Alberto et al. "Classical Affine W -Algebras and the Associated Integrable Hamiltonian Hierarchies for Classical Lie Algebras." Communications in Mathematical Physics 360, 3 (June 2018): 851-918 © 2019 Springer Nature Switzerland AG.
Author's final manuscript
Mathematical Physics, Statistical and Nonlinear Physics