De Sole, A., Kac, V. G. and Valeri, D. (2018) Classical affine W-algebras and the associated integrable Hamiltonian hierarchies for classical Lie algebras. Communications in Mathematical Physics, 360(3), pp. 851-918. (doi: 10.1007/s00220-018-3142-8)
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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.
| Item Type: | Articles |
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| Additional Information: | The first author is supported by National FIRB grant RBFR12RA9W, National PRIN grant 2015ZWST2C, and University grant C26A158K8A, the second author is supported by an NSF grant and the Italian grant C26V1735TJ, and the third author is supported by an NSFC “Research Fund for International Young Scientists” grant and Tsinghua University startup grant. |
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Valeri, Dr Daniele |
| Authors: | De Sole, A., Kac, V. G., and Valeri, D. |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Journal Name: | Communications in Mathematical Physics |
| Publisher: | Springer |
| ISSN: | 0010-3616 |
| ISSN (Online): | 1432-0916 |
| Published Online: | 09 May 2018 |
| Copyright Holders: | Copyright © 2018 Springer-Verlag GmbH Germany, part of Springer Nature |
| First Published: | First published in Communications in Mathematical Physics 360(3): 851-918 |
| Publisher Policy: | Reproduced in accordance with the publisher copyright policy |
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