Generalized Macdonald-Ruijsenaars systems and Double Affine Hecke Algebras

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• Silantyev, A (Glasgow)
• Wednesday 25 March 2009, 11:30-12:30
• Seminar Room 1 Newton Institute.

If you have a question about this talk, please contact Mustapha Amrani.

Discrete Integrable Systems

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 DAH As. We consider submodules in the polynomial representations of DAH As 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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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