The total angular momentum algebra related to the [formula omitted] Dunkl Dirac equation.

We consider the symmetry algebra generated by the total angular momentum operators, appearing as constants of motion of the S 3 Dunkl Dirac equation. The latter is a deformation of the Dirac equation by means of Dunkl operators, in our case associated to the root system A 2 , with corresponding Weyl group S 3 , the symmetric group on three elements. The explicit form of the symmetry algebra in this case is a one-parameter deformation of the classical total angular momentum algebra s o ( 3 ) , incorporating elements of S 3 . This was obtained using recent results on the symmetry algebra for a class of Dirac operators, containing in particular the Dirac–Dunkl operator for arbitrary root system. For this symmetry algebra, we classify all finite-dimensional, irreducible representations and determine the conditions for the representations to be unitarizable. The class of unitary irreducible representations admits a natural realization acting on a representation space of eigenfunctions of the Dirac Hamiltonian. Using a Cauchy–Kowalevski extension theorem we obtain explicit expressions for these eigenfunctions in terms of Jacobi polynomials. [ABSTRACT FROM AUTHOR]