An exceptional symmetry algebra for the 3D Dirac-Dunkl operator
Mathematical Physics
2021-11-04 v1 math.MP
Representation Theory
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 . 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.
Keywords
Cite
@article{arxiv.2009.13904,
title = {An exceptional symmetry algebra for the 3D Dirac-Dunkl operator},
author = {Alexis Langlois-Rémillard and Roy Oste},
journal= {arXiv preprint arXiv:2009.13904},
year = {2021}
}
Comments
7 pages; to be published in Springer Proceedings in Mathematics & Statistics