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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Опубліковано в: :Symmetry, Integrability and Geometry: Methods and Applications
Дата:2023
Автор: Huang, Hau-Wen
Формат: Стаття
Мова:Англійська
Опубліковано: Інститут математики НАН України 2023
Онлайн доступ: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
Цитувати:The Clebsch-Gordan Rule for (₂), the Krawtchouk Algebras and the Hamming Graphs. Hau-Wen Huang. SIGMA 19 (2023), 017, 19 pages

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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Резюме: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.
ISSN:1815-0659