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Dunkl Operators as Covariant Derivatives in a Quantum Principal Bundle
Репозиторій DSpace/Manakin
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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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Dunkl Operators as Covariant Derivatives in a Quantum Principal Bundle
Інший ID:
2010 Mathematics Subject Classification: 20F55; 81R50; 81R60
DOI: http://dx.doi.org/10.3842/SIGMA.2013.040
DOI: http://dx.doi.org/10.3842/SIGMA.2013.040
Посилання:
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.
Підтримка:
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.
Дата:
2013
Переглядів:
560
Завантажень:
231
Анотація:
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.
