Graded limits of minimal affinizations and beyond: the multiplicity free case for type \(E_6\)
We obtain a graded character formula for certain graded modules for the current algebra over a simple Lie algebra of type \(E_6\). For certain values of their highest weight, these modules were conjectured to be isomorphic to the classical limit of the corresponding minimal affinizations of the asso...
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| Дата: | 2018 |
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| Мова: | English |
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Lugansk National Taras Shevchenko University
2018
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-6742018-04-04T09:28:39Z Graded limits of minimal affinizations and beyond: the multiplicity free case for type \(E_6\) Moura, Adriano Pereira, Fernanda minimal affinizations of quantum groups, character formulae, affine Kac-Moody algebras 17B10, 17B70, 20G42 We obtain a graded character formula for certain graded modules for the current algebra over a simple Lie algebra of type \(E_6\). For certain values of their highest weight, these modules were conjectured to be isomorphic to the classical limit of the corresponding minimal affinizations of the associated quantum group. We prove that this is the case under further restrictions on the highest weight. Under another set of conditions on the highest weight, Chari and Greenstein have recently proved that they are projective objects of a full subcategory of the category of graded modules for the current algebra. Our formula applies to all of these projective modules. Lugansk National Taras Shevchenko University 2018-04-04 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/674 Algebra and Discrete Mathematics; Vol 12, No 1 (2011) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/674/208 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| collection |
OJS |
| language |
English |
| topic |
minimal affinizations of quantum groups character formulae affine Kac-Moody algebras 17B10 17B70 20G42 |
| spellingShingle |
minimal affinizations of quantum groups character formulae affine Kac-Moody algebras 17B10 17B70 20G42 Moura, Adriano Pereira, Fernanda Graded limits of minimal affinizations and beyond: the multiplicity free case for type \(E_6\) |
| topic_facet |
minimal affinizations of quantum groups character formulae affine Kac-Moody algebras 17B10 17B70 20G42 |
| format |
Article |
| author |
Moura, Adriano Pereira, Fernanda |
| author_facet |
Moura, Adriano Pereira, Fernanda |
| author_sort |
Moura, Adriano |
| title |
Graded limits of minimal affinizations and beyond: the multiplicity free case for type \(E_6\) |
| title_short |
Graded limits of minimal affinizations and beyond: the multiplicity free case for type \(E_6\) |
| title_full |
Graded limits of minimal affinizations and beyond: the multiplicity free case for type \(E_6\) |
| title_fullStr |
Graded limits of minimal affinizations and beyond: the multiplicity free case for type \(E_6\) |
| title_full_unstemmed |
Graded limits of minimal affinizations and beyond: the multiplicity free case for type \(E_6\) |
| title_sort |
graded limits of minimal affinizations and beyond: the multiplicity free case for type \(e_6\) |
| description |
We obtain a graded character formula for certain graded modules for the current algebra over a simple Lie algebra of type \(E_6\). For certain values of their highest weight, these modules were conjectured to be isomorphic to the classical limit of the corresponding minimal affinizations of the associated quantum group. We prove that this is the case under further restrictions on the highest weight. Under another set of conditions on the highest weight, Chari and Greenstein have recently proved that they are projective objects of a full subcategory of the category of graded modules for the current algebra. Our formula applies to all of these projective modules. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/674 |
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AT mouraadriano gradedlimitsofminimalaffinizationsandbeyondthemultiplicityfreecasefortypee6 AT pereirafernanda gradedlimitsofminimalaffinizationsandbeyondthemultiplicityfreecasefortypee6 |
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2024-04-12T06:25:47Z |
| last_indexed |
2024-04-12T06:25:47Z |
| _version_ |
1796109210571767808 |