Embeddings of the Racah Algebra into the Bannai-Ito Algebra

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Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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Symmetry, Integrability and Geometry: Methods and Applications, 2015, том 11
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dc.contributor.author	Genest, V.X.
dc.contributor.author	Vinet, L.
dc.contributor.author	Zhedanov, A.
dc.date.accessioned	2019-02-13T16:58:46Z
dc.date.available	2019-02-13T16:58:46Z
dc.date.issued	2015
dc.identifier.citation	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.	uk_UA
dc.identifier.issn	1815-0659
dc.identifier.other	2010 Mathematics Subject Classification: 33C80
dc.identifier.other	DOI:10.3842/SIGMA.2015.050
dc.identifier.uri	http://dspace.nbuv.gov.ua/handle/123456789/147119
dc.description.abstract	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.	uk_UA
dc.description.sponsorship	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.	uk_UA
dc.language.iso	en	uk_UA
dc.publisher	Інститут математики НАН України	uk_UA
dc.relation.ispartof	Symmetry, Integrability and Geometry: Methods and Applications
dc.title	Embeddings of the Racah Algebra into the Bannai-Ito Algebra	uk_UA
dc.type	Article	uk_UA
dc.status	published earlier	uk_UA