A SUPERINTEGRABLE MODEL WITH REFLECTIONS ON S^3 AND THE RANK TWO BANNAI-ITO ALGEBRA

Hendrik De Bie, Vincent Xavier Genest, Jean-Michel Lemay, Luc Vinet

Abstract


A quantum superintegrable model with reflections on the three-sphere is presented. Its symmetry algebra is identified with the rank-two Bannai-Ito algebra. It is shown that the Hamiltonian of the system can be constructed from the tensor product of four representations of the superalgebra osp(1|2) and that the superintegrability is naturally understood in that setting. The exact separated solutions are obtained through the Fischer decomposition and a Cauchy-Kovalevskaia extension theorem.

Keywords


Bannai-Ito algebra; Cauchy-Kovalevskaia extension; quantum superintegrable model

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ISSN 1210-2709 (Print)
ISSN 1805-2363 (Online)
Published by the Czech Technical University in Prague