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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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$\mathfrak {osp}(1,2)$ and generalized Bannai–Ito algebras
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by Vincent X. Genest, Luc Lapointe and Luc Vinet PDF
Trans. Amer. Math. Soc. 372 (2019), 4127-4148 Request permission


Generalizations of the (rank-$1$) Bannai–Ito algebra are obtained from a refinement of the grade involution of the Lie superalgebra $\mathfrak {osp}(1,2)$. A hyperoctahedral extension is derived by using a realization of $\mathfrak {osp}(1,2)$ in terms of Dunkl operators associated with the Weyl group $B_3$.
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Additional Information
  • Vincent X. Genest
  • Affiliation: Department of Mathematics, Massachussetts Institute of Technology, Cambridge, Massachusetts 02139
  • MR Author ID: 970414
  • Email:
  • Luc Lapointe
  • Affiliation: Instituto de Matemática y Física, Universidad de Talca, Casilla 747, Talca, Chile
  • MR Author ID: 340905
  • Email:
  • Luc Vinet
  • Affiliation: Centre de Recherches Mathématiques, Université de Montréal, Montréal, Québec H3C 3J7, Canada
  • MR Author ID: 178665
  • ORCID: 0000-0001-6211-7907
  • Email:
  • Received by editor(s): May 26, 2017
  • Received by editor(s) in revised form: August 5, 2018
  • Published electronically: December 7, 2018
  • Additional Notes: The first author holds a postdoctoral fellowship from the Natural Science and Engineering Research Council (NSERC) of Canada.
    The research of the second author is supported by Fondo Nacional de Desarrollo Científico y Tecnológico (FONDECYT) de Chile grant #1170924.
    The third author gratefully acknowledges his support from NSERC through a discovery grant.
  • © Copyright 2018 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 372 (2019), 4127-4148
  • MSC (2010): Primary NUMBER(S)
  • DOI:
  • MathSciNet review: 4009427