Deformed Macdonald-Ruijsenaars operators and super Macdonald polynomials

Sergeev, A.N.; Veselov, Alexander

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Deformed Macdonald-Ruijsenaars operators and super Macdonald polynomials

journal contribution

posted 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.

Funding

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.

History

School

Science

Department

Mathematical Sciences

Published in

COMMUNICATIONS IN MATHEMATICAL PHYSICS

Volume

288

Issue

2

Pages

653 - 675 (23)

Citation

SERGEEV, A.N. and VESELOV, A.P., 2009. Deformed Macdonald-Ruijsenaars operators and super Macdonald polynomials. Communications in Mathematical Physics, 288 (2), pp. 653 - 675.

Publisher

Version

AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Publication date

2009

Notes

This article was published in the journal, Communications in Mathematical Physics [© Springer-Verlag.]. The final publication is available at Springer via http://dx.doi.org/10.1007/s00220-009-0779-3.