## Abstract

The universal Bannai–Ito algebra BI is a unital associative algebra over C generated by X,Y,Z and the relations assert that each of {X,Y}−Z,{Y,Z}−X,{Z,X}−Y commutes with X,Y,Z. Let n≥0 denote an integer. Let M_{n} denote the space of Dunkl monogenics of degree n associated with the reflection group Z_{2}^{3}. When the multiplicity function k is real-valued the space M_{n} supports a BI-module in terms of the symmetries of the spherical Dirac–Dunkl operator. Under the assumption that k is nonnegative, it was shown that dimM_{n}=2(n+1) and M_{n} is isomorphic to a direct sum of two copies of an (n+1)-dimensional irreducible BI-module. In this paper, we generalize the aforementioned result on the BI-module M_{n}.

Original language | English |
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Article number | 115766 |

Journal | Nuclear Physics B |

Volume | 980 |

DOIs | |

State | Published - Jul 2022 |

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