A higher rank Racah algebra and the Z2n Laplace–Dunkl operator. (7th December 2017) - De Bie, Hendrik; Genest, Vincent X; van de Vijver, Wouter; Vinet, Luc
Abstract: A higher rank generalization of the (rank one) Racah algebra is obtained as the symmetry algebra of the Laplace–Dunkl operator associated to the Z 2 n root system. This algebra is also the invariance algebra of the generic superintegrable model on the n -sphere. Bases of Dunkl harmonics are constructed explicitly using a Cauchy–Kovalevskaia theorem. These bases consist of joint eigenfunctions of labelling Abelian subalgebras of the higher rank Racah algebra. A method to obtain expressions for both the connection coefficients between these bases and the action of the symmetries on these bases is presented.