The higher rank q-deformed Bannai-Ito and Askey-Wilson algebra
| Autor: | Wouter van de Vijver, Hendrik De Bie, Hadewijch De Clercq |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Polynomial
Rank (linear algebra) FOS: Physical sciences 01 natural sciences POLYNOMIALS SYSTEMS 16T05 17B37 81R10 81R12 Mathematics::Quantum Algebra 0103 physical sciences Mathematics - Quantum Algebra FOS: Mathematics Quantum Algebra (math.QA) 0101 mathematics Mathematics::Representation Theory Mathematical Physics Mathematics 010102 general mathematics DIFFERENCE-OPERATORS Statistical and Nonlinear Physics Basis (universal algebra) Mathematical Physics (math-ph) Superalgebra Algebra Tensor product Mathematics and Statistics 010307 mathematical physics Isomorphism Symmetry (geometry) Realization (systems) |
| Zdroj: | COMMUNICATIONS IN MATHEMATICAL PHYSICS |
| ISSN: | 0010-3616 1432-0916 |
| Popis: | The $q$-deformed Bannai-Ito algebra was recently constructed in the threefold tensor product of the quantum superalgebra $\mathfrak{osp}_q(1\vert 2)$. 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 $\mathcal{A}_n^q$, 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 $\mathfrak{osp}_q(1\vert 2)$. An explicit realization in terms of $q$-shift operators and reflections is proposed, which will be called the $\mathbb{Z}_2^n$ $q$-Dirac-Dunkl model. The algebra $\mathcal{A}_n^q$ is shown to arise as the symmetry algebra of the constructed $\mathbb{Z}_2^n$ $q$-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 $\mathbf{CK}$-extension and Fischer decomposition. Comment: 38 pages, minor changes and references added |
| Databáze: | OpenAIRE |
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