Quasi-invariants and quantum integrals of the deformed Calogero--Moser systems
Feigin, M. ; Veselov, A. P.
arXiv, 0303026 / Harvested from arXiv
Text on arXiv
The rings of quantum integrals of the generalized Calogero-Moser systems related to the deformed root systems ${\cal A}_n(m)$ and ${\cal C}_n(m,l)$ 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 Poincare series and the deformed $m$-harmonic polynomials are explicitly computed.
Publié le : 2003-03-10
Classification:  Mathematical Physics,  81R12 
@article{0303026,
     author = {Feigin, M. and Veselov, A. P.},
     title = {Quasi-invariants and quantum integrals of the deformed Calogero--Moser
  systems},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0303026}
}

Feigin, M.; Veselov, A. P. Quasi-invariants and quantum integrals of the deformed Calogero--Moser
  systems. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0303026/