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Communications in Mathematical Physics

, Volume 288, Issue 2, pp 653–675 | Cite as

Deformed Macdonald-Ruijsenaars Operators and Super Macdonald Polynomials

  • A. N. Sergeev
  • A. P. VeselovEmail author
Article

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.

Keywords

Symmetric Function Young Diagram Symmetric Polynomial Homogeneous Component Macdonald Polynomial 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of Mathematical SciencesLoughborough UniversityLoughboroughUK
  2. 2.Steklov Institute of MathematicsPetersburgRussia
  3. 3.Landau Institute for Theoretical PhysicsMoscowRussia

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