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Generalized Macdonald-Ruijsenaars systems and Double Affine Hecke Algebras

Silantyev, A (Glasgow)
Wednesday 25 March 2009, 11:30-12:30

Meeting Room 3, CMS


The Double Affine Hecke Algebra (DAHA) is defined by a root system, its basis and by some parameters. The Macdonald-Ruijsenaars systems are known to be obtained from the polynomial representations of DAHAs. We consider submodules in the polynomial representations of DAHAs consisting of functions vanishing on special intersections of shifted mirrors. We derive the generalized Macdonald-Ruijsenaars systems by considering the Dunkl-Cherednik operators acting in the quotient-modules. In the A_n case this recovers Sergeev-Veselov systems, and the corresponding ideals were studied by Kasatani. This is a joint work with M. Feigin.


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