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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2023 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2023
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/211867 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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| _version_ | 1862600679320715264 |
|---|---|
| author | Huang, Hau-Wen |
| author_facet | Huang, Hau-Wen |
| citation_txt | The Clebsch-Gordan Rule for (₂), the Krawtchouk Algebras and the Hamming Graphs. Hau-Wen Huang. SIGMA 19 (2023), 017, 19 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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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| first_indexed | 2026-03-14T02:38:14Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-211867 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-14T02:38:14Z |
| publishDate | 2023 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Huang, Hau-Wen 2026-01-14T09:53:24Z 2023 The Clebsch-Gordan Rule for (₂), the Krawtchouk Algebras and the Hamming Graphs. Hau-Wen Huang. SIGMA 19 (2023), 017, 19 pages 1815-0659 2020 Mathematics Subject Classification: 05E30; 16G30; 16S30; 33D45 arXiv:2106.06857 https://nasplib.isofts.kiev.ua/handle/123456789/211867 https://doi.org/10.3842/SIGMA.2023.017 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. The author would like to thank the anonymous referees for insightful suggestions to improve the paper and bring his attention to [13]. Additionally, the author thanks Dr. Luc Vinet for bringing [1, 2, 9] to his attention. The research is supported by the Ministry of Science and Technology of Taiwan under the project MOST 110-2115-M-008-008-MY2. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications The Clebsch-Gordan Rule for (₂), the Krawtchouk Algebras and the Hamming Graphs Article published earlier |
| spellingShingle | The Clebsch-Gordan Rule for (₂), the Krawtchouk Algebras and the Hamming Graphs Huang, Hau-Wen |
| title | The Clebsch-Gordan Rule for (₂), the Krawtchouk Algebras and the Hamming Graphs |
| title_full | The Clebsch-Gordan Rule for (₂), the Krawtchouk Algebras and the Hamming Graphs |
| title_fullStr | The Clebsch-Gordan Rule for (₂), the Krawtchouk Algebras and the Hamming Graphs |
| title_full_unstemmed | The Clebsch-Gordan Rule for (₂), the Krawtchouk Algebras and the Hamming Graphs |
| title_short | The Clebsch-Gordan Rule for (₂), the Krawtchouk Algebras and the Hamming Graphs |
| title_sort | clebsch-gordan rule for (₂), the krawtchouk algebras and the hamming graphs |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211867 |
| work_keys_str_mv | AT huanghauwen theclebschgordanrulefor2thekrawtchoukalgebrasandthehamminggraphs AT huanghauwen clebschgordanrulefor2thekrawtchoukalgebrasandthehamminggraphs |