Dunkl Operators as Covariant Derivatives in a Quantum Principal Bundle
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Dunkl Operators as Covariant Derivatives in a Quantum Principal Bundle
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| Creator |
Đurđevich, M.
Sontz, S.B. |
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| Description |
A quantum principal bundle is constructed for every Coxeter group acting on a finite-dimensional Euclidean space E, and then a connection is also defined on this bundle. The covariant derivatives associated to this connection are the Dunkl operators, originally introduced as part of a program to generalize harmonic analysis in Euclidean spaces. This gives us a new, geometric way of viewing the Dunkl operators. In particular, we present a new proof of the commutativity of these operators among themselves as a consequence of a geometric property, namely, that the connection has curvature zero.
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| Date |
2019-02-19T18:30:30Z
2019-02-19T18:30:30Z 2013 |
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| Type |
Article
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| Identifier |
Dunkl Operators as Covariant Derivatives in a Quantum Principal Bundle / M. Đurđevich, S.B. Sontz // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 32 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 20F55; 81R50; 81R60 DOI: http://dx.doi.org/10.3842/SIGMA.2013.040 http://dspace.nbuv.gov.ua/handle/123456789/149199 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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