Speaker: Luc Vinet, Université de Montréal
Date: Tue, Sep 08, 2015
Time: 10:00 - 11:00
Venue: Middle Meeting Room
Title: A Dirac-Dunkl equation on $S^2$ and the Bannai-Ito algebra
The Dirac-Dunkl operator on the $2$-sphere associated to the $Z^3_2$ reflection group is considered. Its symmetries are found and are shown to generate the Bannai-Ito algebra. Representations of the Bannai-Ito algebra are constructed using ladder operators. Eigenfunctions of the spherical Dirac-Dunkl operator are obtained using a Cauchy-Kovalevskaia extension theorem. These eigenfunctions, which correspond to Dunkl monogenics, are seen to support finite-dimensional irreducible representations of the Bannai-Ito algebra.