Deformed Macdonald-Ruijsenaars operators and super Macdonald polynomials
journal contributionposted on 2014-11-10, 14:26 authored by A.N. Sergeev, Alexander VeselovAlexander Veselov
It is shown that the deformed Macdonald-Ruijsenaars operators can be described as the restrictions on certain affine subvarieties of the usual Macdonald- Ruijsenaars operator in infinite number of variables. The ideals of these varieties are shown to be generated by the Macdonald polynomials related to Young diagrams with special geometry. The super Macdonald polynomials and their shifted version are introduced; the combinatorial formulas for them are given.
This work has been partially supported by the EPSRC (grant EP/E004008/1), European Union through the FP6 Marie Curie RTN ENIGMA (Contract number MRTN-CT-2004-5652) and ESF programme MISGAM.
- Mathematical Sciences