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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Abstract
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 |
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| Status: | Published |
| Refereed: | Yes |
| 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 |
| Publisher: | Elsevier |
| ISSN: | 0001-8708 |
| 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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