Classical Affine W -Algebras and the Associated Integrable Hamiltonian Hierarchies for Classical Lie Algebras
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1705.10103.pdf
Description
Accepted version
Size
718.59 KB
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Checksum (MD5)
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Author(s)
De Sole, Alberto
Kac, Victor
Valeri, Daniele
Date Issued
June 2018
Journal
Communications in Mathematical Physics
Publisher
Springer Berlin Heidelberg
Citation
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.
Version
Author's final manuscript
Abstract
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.
Subjects
Mathematical Physics
Statistical and Nonlinear Physics
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1007/s00220-018-3142-8
