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Dunkl Operators as Covariant Derivatives in a Quantum Principal Bundle
- Source :
- SIGMA 9 (2013), 040, 29 pages
- Publication Year :
- 2011
-
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.
Details
- Database :
- arXiv
- Journal :
- SIGMA 9 (2013), 040, 29 pages
- Publication Type :
- Report
- Accession number :
- edsarx.1108.3769
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.3842/SIGMA.2013.040