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Dunkl Operators as Covariant Derivatives in a Quantum Principal Bundle
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2013, том 9
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| dc.contributor.author | Đurđevich, M. | |
| dc.contributor.author | Sontz, S.B. | |
| dc.date.accessioned | 2019-02-19T18:30:30Z | |
| dc.date.available | 2019-02-19T18:30:30Z | |
| dc.date.issued | 2013 | |
| dc.identifier.citation | 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. | uk_UA |
| dc.identifier.issn | 1815-0659 | |
| dc.identifier.other | 2010 Mathematics Subject Classification: 20F55; 81R50; 81R60 | |
| dc.identifier.other | DOI: http://dx.doi.org/10.3842/SIGMA.2013.040 | |
| dc.identifier.uri | http://dspace.nbuv.gov.ua/handle/123456789/149199 | |
| dc.description.abstract | 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. | uk_UA |
| dc.description.sponsorship | 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. | uk_UA |
| dc.language.iso | en | uk_UA |
| dc.publisher | Інститут математики НАН України | uk_UA |
| dc.relation.ispartof | Symmetry, Integrability and Geometry: Methods and Applications | |
| dc.title | Dunkl Operators as Covariant Derivatives in a Quantum Principal Bundle | uk_UA |
| dc.type | Article | uk_UA |
| dc.status | published earlier | uk_UA |
