Letters in Mathematical Physics

, Volume 105, Issue 12, pp 1725–1734 | Cite as

The Equitable Presentation of \({\mathfrak{osp}_q(1|2)}\) and a q-Analog of the Bannai–Ito Algebra

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Abstract

The equitable presentation of the quantum superalgebra \({\mathfrak{osp}_q(1|2)}\), in which all generators appear on an equal footing, is exhibited. It is observed that in their equitable presentations, the quantum algebras \({\mathfrak{osp}_q(1|2)}\) and \({\mathfrak{sl}_q(2)}\) are related to one another by the formal transformation \({q\rightarrow -q}\). A q-analog of the Bannai–Ito algebra is shown to arise as the covariance algebra of \({\mathfrak{osp}_q(1|2)}\).

Keywords

quantum superalgebra \({\mathfrak{osp}_{q}(1|2)}\) Bannai–Ito algebra 

Mathematics Subject Classification

17B37 20G42 81R50 
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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Vincent X. Genest
    • 1
  • Luc Vinet
    • 1
  • Alexei Zhedanov
    • 2
  1. 1.Centre de recherches mathématiquesUniversité de MontréalMontrealCanada
  2. 2.Donetsk Institute for Physics and TechnologyDonetskUkraine

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