Linear Independence for ⁽¹⁾₁ by Using ⁽¹⁾₂
In the previous paper, the authors proved linear independence of the combinatorial spanning set for the standard ⁽¹⁾ℓ-module (Λ₀) by establishing a connection with the combinatorial basis of Feigin-Stoyanovsky's type subspace (Λ₀) of ⁽¹⁾2ℓ-module (Λ₀). In this note, we extend this argument for...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2025 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2025
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/214171 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Linear Independence for ⁽¹⁾₁ by Using ⁽¹⁾₂. Mirko Primc and Goran Trupčević. SIGMA 21 (2025), 071, 6 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862695567289745408 |
|---|---|
| author | Primc, Mirko Trupčević, Goran |
| author_facet | Primc, Mirko Trupčević, Goran |
| citation_txt | Linear Independence for ⁽¹⁾₁ by Using ⁽¹⁾₂. Mirko Primc and Goran Trupčević. SIGMA 21 (2025), 071, 6 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | In the previous paper, the authors proved linear independence of the combinatorial spanning set for the standard ⁽¹⁾ℓ-module (Λ₀) by establishing a connection with the combinatorial basis of Feigin-Stoyanovsky's type subspace (Λ₀) of ⁽¹⁾2ℓ-module (Λ₀). In this note, we extend this argument for ⁽¹⁾₁ ≅ ⁽¹⁾₁ to all standard ⁽¹⁾₁-modules (Λ). In the proof, we use a coefficient of an intertwining operator of the type ((Λ₂)(Λ₁) (Λ₁)) for standard ⁽¹⁾₂-modules.
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| first_indexed | 2026-03-18T06:06:51Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-214171 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-18T06:06:51Z |
| publishDate | 2025 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Primc, Mirko Trupčević, Goran 2026-02-19T16:04:27Z 2025 Linear Independence for ⁽¹⁾₁ by Using ⁽¹⁾₂. Mirko Primc and Goran Trupčević. SIGMA 21 (2025), 071, 6 pages 1815-0659 2020 Mathematics Subject Classification: 17B67; 17B69 arXiv:2504.15597 https://nasplib.isofts.kiev.ua/handle/123456789/214171 https://doi.org/10.3842/SIGMA.2025.071 In the previous paper, the authors proved linear independence of the combinatorial spanning set for the standard ⁽¹⁾ℓ-module (Λ₀) by establishing a connection with the combinatorial basis of Feigin-Stoyanovsky's type subspace (Λ₀) of ⁽¹⁾2ℓ-module (Λ₀). In this note, we extend this argument for ⁽¹⁾₁ ≅ ⁽¹⁾₁ to all standard ⁽¹⁾₁-modules (Λ). In the proof, we use a coefficient of an intertwining operator of the type ((Λ₂)(Λ₁) (Λ₁)) for standard ⁽¹⁾₂-modules. We are deeply honored to contribute this work to an issue dedicated to Jim Lepowsky– an exceptional mathematician whose work has significantly shaped our scientific paths, a wonderful friend, and one of the kindest people that we know. This work was supported by the project “Implementation of cutting-edge research and its application as part of the Scientific Center of Excellence for Quantum and Complex Systems, and Representations of Lie Algebras”, PK.1.1.02, European Union, European Regional Development Fund. Also, this work has been supported by the Croatian Science Foundation under the project IP-2022-10-9006. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Linear Independence for ⁽¹⁾₁ by Using ⁽¹⁾₂ Article published earlier |
| spellingShingle | Linear Independence for ⁽¹⁾₁ by Using ⁽¹⁾₂ Primc, Mirko Trupčević, Goran |
| title | Linear Independence for ⁽¹⁾₁ by Using ⁽¹⁾₂ |
| title_full | Linear Independence for ⁽¹⁾₁ by Using ⁽¹⁾₂ |
| title_fullStr | Linear Independence for ⁽¹⁾₁ by Using ⁽¹⁾₂ |
| title_full_unstemmed | Linear Independence for ⁽¹⁾₁ by Using ⁽¹⁾₂ |
| title_short | Linear Independence for ⁽¹⁾₁ by Using ⁽¹⁾₂ |
| title_sort | linear independence for ⁽¹⁾₁ by using ⁽¹⁾₂ |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/214171 |
| work_keys_str_mv | AT primcmirko linearindependencefor11byusing12 AT trupcevicgoran linearindependencefor11byusing12 |