Type: Seminar

Distribution: World

Expiry: 8 May 2017

CalTitle1: Algebra Seminar: On the algebra of symmetries of Dirac operators

Auth: kevinc@pkevinc.pc (assumed)

Hendrik De Bie (Ghent University) Friday 7 April, 12-1pm, Place: Carslaw 375 Title: On the algebra of symmetries of Dirac operators Abstract: 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 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 (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 (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.