A superintegrable model with reflections on Sn−1 and the higher rank Bannai–Ito algebra. (10th April 2017)

• Record Type: Journal Article
• Authors: De Bie, Hendrik; Genest, Vincent X; Lemay, Jean-Michel; Vinet, Luc
• Is Part Of: Journal of physics. Volume 50:Number 19(2017)
• Publication Date: 2017-04-10
• Subjects: superintegrable model -- (n − 1)-sphere -- Bannai–Ito algebra; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/aa65e1
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: A quantum superintegrable model with reflections on the ( n − 1)-sphere is presented. Its symmetry algebra is identified with the higher rank generalization of the Bannai–Ito algebra. It is shown that the Hamiltonian of the system can be constructed from the tensor product of n representations of the superalgebra o s p ( 1 | 2 ) and that the superintegrability is naturally understood in that setting. The separated solutions are obtained through the Fischer decomposition and a Cauchy–Kovalevskaia extension theorem.