The Clebsch-Gordan Rule for (₂), the Krawtchouk Algebras and the Hamming Graphs
Let ≥ 1 and ≥ 3 be two integers. Let () = (, ) denote the -dimensional Hamming graph over a q-element set. Let () denote the Terwilliger algebra of (). Let () denote the standard ()-module. Let ω denote a complex scalar. We consider a unital associative algebra ω defined by generators and relation...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2023 |
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| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2023
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211867 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | The Clebsch-Gordan Rule for (₂), the Krawtchouk Algebras and the Hamming Graphs. Hau-Wen Huang. SIGMA 19 (2023), 017, 19 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | Let ≥ 1 and ≥ 3 be two integers. Let () = (, ) denote the -dimensional Hamming graph over a q-element set. Let () denote the Terwilliger algebra of (). Let () denote the standard ()-module. Let ω denote a complex scalar. We consider a unital associative algebra ω defined by generators and relations. The generators are and . The relations are ² − 2 + ² = + ω, ² − 2 + ² = + ω. The algebra ω is the case of the Askey-Wilson algebras corresponding to the Krawtchouk polynomials. The algebra ω is isomorphic to U(₂) when ω² ≠ 1. We view () as a ₁₋₂/-module. We apply the Clebsch-Gordan rule for U(₂) to decompose () into a direct sum of irreducible ()-modules.
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| ISSN: | 1815-0659 |