The higher rank q-deformed Bannai-Ito and Askey-Wilson algebra

The q-deformed Bannai-Ito algebra was recently constructed in the threefold tensor product of the quantum superalgebra osp(q) (1 | 2). It turned out to be isomorphic to the Askey-Wilson algebra. In the present paper these results will be extended to higher rank. The rank n - 2 q-Bannai-Ito algebra A(n)(q), which by the established isomorphism also yields a higher rank version of the Askey-Wilson algebra, is constructed in the n-fold tensor product of osp(q) (1 | 2). An explicit realization in terms of q-shift operators and reflections is proposed, which will be called the Z(2)(n) q-Dirac-Dunkl model. The algebra A(n)(q) is shown to arise as the symmetry algebra of the constructed Z(2)(n) q-Dirac-Dunkl operator and to act irreducibly on modules of its polynomial null-solutions. An explicit basis for these modules is obtained using a q-deformed CK-extension and Fischer decomposition