Dunkl Operators as Covariant Derivatives in a Quantum Principal Bundle
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 gen...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2013 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2013
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/149199 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862741649200775168 |
|---|---|
| author | Đurđevich, M. Sontz, S.B. |
| author_facet | Đurđevich, M. Sontz, S.B. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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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| first_indexed | 2025-12-07T20:21:01Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-149199 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T20:21:01Z |
| publishDate | 2013 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Đurđevich, M. Sontz, S.B. 2019-02-19T18:30:30Z 2019-02-19T18:30:30Z 2013 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 https://nasplib.isofts.kiev.ua/handle/123456789/149199 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. The second author wishes to thank the Instituto de Matem´aticas (UNAM) and the first author
 for their generous hospitality during various academic visits during which this paper was written. The first author would like to express his gratitude to the Centro de Investigaciones en
 Matem´aticas (CIMAT, Guanajuato) and the second author for their kind hospitality during
 several academic visits during which the roots of the conceptual framework for this research
 were established. We both gratefully thank the referees for their comments which have led to
 several clarifications and improvements. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Dunkl Operators as Covariant Derivatives in a Quantum Principal Bundle Article published earlier |
| spellingShingle | Dunkl Operators as Covariant Derivatives in a Quantum Principal Bundle Đurđevich, M. Sontz, S.B. |
| title | Dunkl Operators as Covariant Derivatives in a Quantum Principal Bundle |
| title_full | Dunkl Operators as Covariant Derivatives in a Quantum Principal Bundle |
| title_fullStr | Dunkl Operators as Covariant Derivatives in a Quantum Principal Bundle |
| title_full_unstemmed | Dunkl Operators as Covariant Derivatives in a Quantum Principal Bundle |
| title_short | Dunkl Operators as Covariant Derivatives in a Quantum Principal Bundle |
| title_sort | dunkl operators as covariant derivatives in a quantum principal bundle |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149199 |
| work_keys_str_mv | AT đurđevichm dunkloperatorsascovariantderivativesinaquantumprincipalbundle AT sontzsb dunkloperatorsascovariantderivativesinaquantumprincipalbundle |