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Embeddings of the Racah Algebra into the Bannai-Ito Algebra
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- Symmetry, Integrability and Geometry: Methods and Applications, 2015, том 11
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Embeddings of the Racah Algebra into the Bannai-Ito Algebra
Інший ID:
2010 Mathematics Subject Classification: 33C80
DOI:10.3842/SIGMA.2015.050
DOI:10.3842/SIGMA.2015.050
Посилання:
Embeddings of the Racah Algebra into the Bannai-Ito Algebra / V.X. Genest, L. Vinet, A. Zhedanov // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 20 назв. — англ.
Підтримка:
This paper is a contribution to the Special Issue on Exact Solvability and Symmetry Avatars in honour of
Luc Vinet. The full collection is available at http://www.emis.de/journals/SIGMA/ESSA2014.html.
The authors would like to thank an anonymous referee for pointing out that the embedding of the
Racah algebra in the Bannai–Ito algebra proposed in section two holds in the abstract. V.X.G. is
supported by the Natural Science and Engineering Research Council of Canada (NSERC). The
research of L.V. is supported in part by NSERC. A.Z. wishes to thank the Centre de Recherches
Math´ematiques for its hospitality.
Дата:
2015
Переглядів:
510
Завантажень:
250
Анотація:
Embeddings of the Racah algebra into the Bannai-Ito algebra are proposed in two realizations. First, quadratic combinations of the Bannai-Ito algebra generators in their standard realization on the space of polynomials are seen to generate a central extension of the Racah algebra. The result is also seen to hold independently of the realization. Second, the relationship between the realizations of the Bannai-Ito and Racah algebras by the intermediate Casimir operators of the osp(1|2) and su(1,1) Racah problems is established. Equivalently, this gives an embedding of the invariance algebra of the generic superintegrable system on the two-sphere into the invariance algebra of its extension with reflections, which are respectively isomorphic to the Racah and Bannai-Ito algebras.
