The space of Dunkl monogenics associated with Z₂³

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 Z₂³. 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 dim⁡M_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.