Quasi-invariants and quantum integrals of the deformed Calogero-Moser systems

Feigin, M. and Veselov, A.P. (2003) Quasi-invariants and quantum integrals of the deformed Calogero-Moser systems. International Mathematics Research Notices, 2003(46), pp. 2487-2511. (doi: 10.1155/S1073792803130826)

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Publisher's URL: http://dx.doi.org/10.1155/S1073792803130826


The rings of quantum integrals of the generalized Calogero-Moser systems related to the deformed root systems An(m) and Cn(m,l) with integer multiplicities and corresponding algebras of quasi-invariants are investigated. In particular, it is shown that these algebras are finitely generated and free as the modules over certain polynomial subalgebras (Cohen-Macaulay property). The proof follows the scheme proposed by Etingof and Ginzburg in the Coxeter case. For two-dimensional systems the corresponding Poincaré series and the deformed m-harmonic polynomials are explicitly computed.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Feigin, Professor Misha
Authors: Feigin, M., and Veselov, A.P.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:International Mathematics Research Notices
ISSN (Online):1687-0247

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