Algebra Seminar: De Bie -- On the algebra of symmetries of Dirac operators

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.