# The kernel of the Dunkl Dirac operator as a module for the Bannai-Ito algebra

Presenter: Hendrik De Bie, Ghent University, Belgium

Joint work with Vincent Genest, Luc Vinet

In this talk I will discuss how the CK or Cauchy-Kowalewska extension procedure can be developed for the Dunkl Dirac operator related to the reflection group $(Z_2)^m$. This will be used to construct an explicit basis for the kernel in dimension three, expressed in terms of Jacobi polynomials. In turn, by determining the symmetries of the Dunkl Dirac operator in dimension three, we obtain an unexpected connection with the Bannai-Ito algebra and with a scalar operator that also factorizes the Dunkl Laplacian. A detailed comparison will be given between the two approaches.