# Combinatorics Seminar 2015

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: paper

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