Deformed Macdonald-Ruijsenaars operators and super Macdonald polynomials

Details Deformed Macdonald-Ruijsenaars operators and super Macdonald polynomials Deformed Macdonald-Ruijsenaars operators and super Macdonald polynomials

2007-07-20

arxiv.org/abs/0707.3129v2

Mathematics

Quantum Algebra

Revised version after minor corrections

Scientific paper

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.

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