A higher rank Racah algebra and the Z2n Laplace–Dunkl operator. (7th December 2017)

• Record Type: Journal Article
• Authors: De Bie, Hendrik; Genest, Vincent X; van de Vijver, Wouter; Vinet, Luc
• Is Part Of: Journal of physics. Volume 51:Number 2(2018)
• Publication Date: 2017-12-07
• Subjects: Racah algebra -- Dunkl operators -- integrable systems -- connection coefficients; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/aa9756
• Languages: English
• ISSNs: 1751-8113

Abstract

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.