Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

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



$ \mathfrak{osp}(1,2)$ and generalized Bannai-Ito algebras

Authors: Vincent X. Genest, Luc Lapointe and Luc Vinet
Journal: Trans. Amer. Math. Soc.
MSC (2010): Primary 17B37; Secondary 81R05
Published electronically: December 7, 2018
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: 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$.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 17B37, 81R05

Retrieve articles in all journals with MSC (2010): 17B37, 81R05

Additional Information

Vincent X. Genest
Affiliation: Department of Mathematics, Massachussetts Institute of Technology, Cambridge, Massachusetts 02139

Luc Lapointe
Affiliation: Instituto de Matemática y Física, Universidad de Talca, Casilla 747, Talca, Chile

Luc Vinet
Affiliation: Centre de Recherches Mathématiques, Université de Montréal, Montréal, Québec H3C 3J7, Canada

Keywords: Bannai--Ito algebra
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.
Article copyright: © Copyright 2018 American Mathematical Society