**Speaker**: Luc Vinet, UniversitÃ© de MontrÃ©al

**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

**Abstract**:

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.

**Paper**:
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