Deformed Macdonald-Ruijsenaars operators and super Macdonald polynomials
A.N. Sergeev, A.P. Veselov
TL;DR
This paper introduces super Macdonald polynomials, describes deformed Macdonald-Ruijsenaars operators as restrictions on affine subvarieties, and provides combinatorial formulas for these polynomials, advancing the understanding of their algebraic structure.
Contribution
It characterizes deformed Macdonald-Ruijsenaars operators as restrictions on affine subvarieties and introduces super Macdonald polynomials with explicit combinatorial formulas.
Findings
Deformed operators are restrictions on affine subvarieties.
Ideals generated by Macdonald polynomials with special Young diagram geometry.
Explicit combinatorial formulas for super Macdonald polynomials.
Abstract
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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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Advanced Combinatorial Mathematics