University of Sydney Algebra Seminar

Hendrik De Bie (Ghent University)

Friday 7 April, 12-13pm, Place: Carslaw 375

On the algebra of symmetries of Dirac operators.

It is well-known that the n dimensional Laplace or Dirac equation has the angular momentum operators as symmetries. These operators generate the Lie algebra $\mathfrak{so}(n)$. The situation becomes quite a bit more complicated (and interesting) if a deformation of the Dirac equation is considered. We are interested in the case where the deformation comes from the action of a finite reflection group. When the group is $({\mathbb{Z}}_2{)}^n$, this leads to the Bannai-Ito algebra. The case of arbitrary reflection groups is more complicated and uses techniques from Wigner quantization. I will explain both the $({\mathbb{Z}}_2{)}^n$ and the more general case. This is based on joint work with V. Genest, L. Vinet, J. Van der Jeugt and R. Oste.