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arXiv · 2009.13904

An exceptional symmetry algebra for the 3D Dirac-Dunkl operator

Alexis Langlois-Rémillard·Roy Oste
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Abstract

We initiate the study of an algebra of symmetries for the 3D Dirac-Dunkl operator associated with the Weyl group of the exceptional root system $G_2$. For this symmetry algebra, we give both an abstract definition and an explicit realisation. We then construct ladder operators, using an intermediate result we prove for the Dirac-Dunkl symmetry algebra associated with arbitrary finite reflection group acting on a three-dimensional space.

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Alexis Langlois-Rémillard, Roy Oste. 2020-09-29. An exceptional symmetry algebra for the 3D Dirac-Dunkl operator. https://doi.org/10.1007/978-981-15-7775-8_30

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