Centralizers of the superalgebra osp(1|2) : the Brauer algebra as a quotient of the Bannai–Ito algebra

Nicolas Crampé; Luc Frappat; Luc Vinet

Centralizers of the superalgebra osp(1|2) : the Brauer algebra as a quotient of the Bannai–Ito algebra

Nicolas Crampé ^{1, 2, *} Luc Frappat ^{3, *} Luc Vinet ²

* Corresponding author

1 IDP - Institut Denis Poisson

2 CRM - Centre de Recherches Mathématiques [Montréal]

3 LAPTH - Laboratoire d'Annecy-le-Vieux de Physique Théorique

Abstract : We provide an explicit isomorphism between a quotient of the Bannai-Ito algebra and the Brauer algebra. We clarify also the connection with the action of the Lie superalgebra osp(1|2) on the threefold tensor product of its fundamental representation. Finally, a conjecture is proposed to describe the centralizer of osp(1|2) acting on three copies of an arbitrary finite irreducible representation in terms of a quotient of the Bannai-Ito algebra. To the fond memory of Peter Freund, a much esteemed scientist who always generously shared his immense culture.

Document type :

Journal articles

Domain :

Mathematics [math] / Representation Theory [math.RT]

Mathematics [math] / Quantum Algebra [math.QA]

Complete list of metadatas

Cited literature [19 references] Display Hide Download

https://hal-univ-tours.archives-ouvertes.fr/hal-02305470
Contributor : Sandrine Renard-Riccetti <>
Submitted on : Friday, October 4, 2019 - 11:18:23 AM
Last modification on : Thursday, October 10, 2019 - 1:05:03 AM

1906.03936.pdf

Files produced by the author(s)

Centralizers of the superalgebra osp(1|2) : the Brauer algebra as a quotient of the Bannai–Ito algebra

File

Identifiers

Collections

Citation

Export

Metrics

19

30

Contact

Centralizers of the superalgebra osp(1|2) : the Brauer algebra as a quotient of the Bannai–Ito algebra

File

Identifiers

Collections

Citation

Export

Share

Metrics

19

30

Contact