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

A superintegrable model with reflections on s^3 and the rank two bannai-ito algebra

Číslo: 3/2016
Periodikum: Acta Polytechnica
DOI: 10.14311/AP.2016.56.0166

Klíčová slova: Bannai-Ito algebra; Cauchy-Kovalevskaia extension; quantum superintegrable model, Bannai-Ito algebra; Cauchy-Kovalevskaia rozšíření; Kvantový superintegrabilní model

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Anotace: 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.