A filtration on the ring of Laurent polynomials and representations of the general linear Lie algebra
We first present a filtration on the ring \(L_n\) of Laurent polynomials such that the direct sum decomposition of its associated graded ring \(gr L_n\) agrees with the direct sum decomposition of \(gr L_n\), as a module over the complex general linear Lie algebra \(\mathfrak{gl}(n)\), into its simp...
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| Дата: | 2021 |
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| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2021
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1304 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-13042021-11-09T03:53:16Z A filtration on the ring of Laurent polynomials and representations of the general linear Lie algebra Choi, C. Kim, S. Seo, H. Laurent polynomial, filtration, general linear Lie algebra, weight module 16S34, 16W70, 17B10, 17B45 We first present a filtration on the ring \(L_n\) of Laurent polynomials such that the direct sum decomposition of its associated graded ring \(gr L_n\) agrees with the direct sum decomposition of \(gr L_n\), as a module over the complex general linear Lie algebra \(\mathfrak{gl}(n)\), into its simple submodules. Next, generalizing the simple modules occurring in the associated graded ring \(gr L_n\), we give some explicit constructions of weight multiplicity-free irreducible representations of \(\mathfrak{gl}(n)\). Lugansk National Taras Shevchenko University 2021-11-09 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1304 10.12958/adm1304 Algebra and Discrete Mathematics; Vol 32, No 1 (2021) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1304/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1304/838 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1304/839 Copyright (c) 2021 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| collection |
OJS |
| language |
English |
| topic |
Laurent polynomial filtration general linear Lie algebra weight module 16S34 16W70 17B10 17B45 |
| spellingShingle |
Laurent polynomial filtration general linear Lie algebra weight module 16S34 16W70 17B10 17B45 Choi, C. Kim, S. Seo, H. A filtration on the ring of Laurent polynomials and representations of the general linear Lie algebra |
| topic_facet |
Laurent polynomial filtration general linear Lie algebra weight module 16S34 16W70 17B10 17B45 |
| format |
Article |
| author |
Choi, C. Kim, S. Seo, H. |
| author_facet |
Choi, C. Kim, S. Seo, H. |
| author_sort |
Choi, C. |
| title |
A filtration on the ring of Laurent polynomials and representations of the general linear Lie algebra |
| title_short |
A filtration on the ring of Laurent polynomials and representations of the general linear Lie algebra |
| title_full |
A filtration on the ring of Laurent polynomials and representations of the general linear Lie algebra |
| title_fullStr |
A filtration on the ring of Laurent polynomials and representations of the general linear Lie algebra |
| title_full_unstemmed |
A filtration on the ring of Laurent polynomials and representations of the general linear Lie algebra |
| title_sort |
filtration on the ring of laurent polynomials and representations of the general linear lie algebra |
| description |
We first present a filtration on the ring \(L_n\) of Laurent polynomials such that the direct sum decomposition of its associated graded ring \(gr L_n\) agrees with the direct sum decomposition of \(gr L_n\), as a module over the complex general linear Lie algebra \(\mathfrak{gl}(n)\), into its simple submodules. Next, generalizing the simple modules occurring in the associated graded ring \(gr L_n\), we give some explicit constructions of weight multiplicity-free irreducible representations of \(\mathfrak{gl}(n)\). |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2021 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1304 |
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2024-04-12T06:26:03Z |
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2024-04-12T06:26:03Z |
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1796109147622604800 |