Generalized elliptic Calogero-Moser systems from elliptic Dunkl operators

Alexey Silantyev (University of Leeds)

Tuesday 8th April, 2014 15:00-16:00 Maths 326


In the work of Misha Feigin (2008) the generalized (deformed) Calogero-Moser systems for any finite Coxeter group were obtained by using Dunkl operators (rational case). As the Heckman construction of the (rational) Calogero-Moser systems uses the Dunkl operators, the generalized systems are obtained from Dunkl operators considered in a quotient space over invariant parabolic ideals. The same parabolic ideals are invariant under the action of the (gauged) elliptic Dunkl operators obtained by V.M. Buchstaber, G. Felder, A. Veselov (1994) and by P. Etingof, X. Ma (2007) for more general case. We have constructed the generalized elliptic Calogero-Moser systems generalizing the construction of G. Felder, A. Veselov, P. Etingof, X. Ma (2010) done for the ordinary elliptic Calogero-Moser systems. This is a joint work with Misha Feigin.

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