On Dunkl angular momenta algebra

On Dunkl angular momenta algebra

Bibliographic Details
Parent link:Journal of High Energy Physics: Scientific Journal
Vol. 2015, Iss. 11.— 2015.— [107, 22 p.]
Main Author: Feigin M. Misha
Corporate Author: Национальный исследовательский Томский политехнический университет (ТПУ) Физико-технический институт (ФТИ) Кафедра высшей математики и математической физики (ВММФ)
Other Authors: Akopyan (Hakobyan) T. S. Tigran Stepanovich
Summary:Title screen
We consider the quantum angular momentum generators, deformed by means of the Dunkl operators. Together with the reflection operators they generate a subalgebra in the rational Cherednik algebra associated with a finite real reflection group. We find all the defining relations of the algebra, which appear to be quadratic, and we show that the algebra is of Poincarй-Birkhoff-Witt (PBW) type. We show that this algebra contains the angular part of the Calogero-Moser Hamiltonian and that together with constants it generates the centre of the algebra. We also consider the gl(N ) version of the subalge-bra of the rational Cherednik algebra and show that it is a non-homogeneous quadratic algebra of PBW type as well. In this case the central generator can be identified with the usual Calogero-Moser Hamiltonian associated with the Coxeter group in the harmonic confinement.
Режим доступа: по договору с организацией-держателем ресурса
Language:English
Published: 2015
Series:Regular Article - Theoretical Physics
Subjects:
электронный ресурс
труды учёных ТПУ
интегрируемые уравнения
физика
Online Access:http://dx.doi.org/10.1007/JHEP11(2015)107
Format: Electronic Book Chapter
KOHA link:https://koha.lib.tpu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=646391

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