Generalized Macdonald-Ruijsenaars systems

Feigin, M. and Silantyev, A. (2014) Generalized Macdonald-Ruijsenaars systems. Advances in Mathematics, 250, pp. 144-192. (doi: 10.1016/j.aim.2013.09.001)

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We consider the polynomial representation of Double Affine Hecke Algebras (DAHAs) and construct its submodules as ideals of functions vanishing on the special collections of affine planes. This generalizes certain results of Kasatani in types A_n, (C_n^\vee,C_n). We obtain commutative algebras of difference operators given by the action of invariant combinations of Cherednik-Dunkl operators in the corresponding quotient modules of the polynomial representation. This gives known and new generalized Macdonald-Ruijsenaars systems. Thus in the cases of DAHAs of types A_n and (C_n^\vee,C_n) we derive Chalykh-Sergeev-Veselov operators and a generalization of the Koornwinder operator respectively, together with complete sets of quantum integrals in the explicit form.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Silantyev, Mr Alexey and Feigin, Professor Misha
Authors: Feigin, M., and Silantyev, A.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics
Journal Name:Advances in Mathematics
ISSN (Online):1090-2082
Copyright Holders:Copyright © 2013 The Authors
First Published:First published in Advances in Mathematics 250:144-192
Publisher Policy:Reproduced under a Creative Commons License

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
468861Calogero-Moser systems, Cherednik algebras and Frobenius structuresMikhail FeiginEngineering & Physical Sciences Research Council (EPSRC)EP/F032889/1M&S - MATHEMATICS