Induced Modules for Affine Lie Algebras
We study induced modules of nonzero central charge with arbitrary multiplicities over affine Lie algebras. For a given pseudo parabolic subalgebra P of an affine Lie algebra G, our main result establishes the equivalence between a certain category of P-induced G-modules and the category of weight P-...
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| Дата: | 2009 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2009
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/149179 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Induced Modules for Affine Lie Algebras / V. Futorny, I. Kashuba // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 22 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-149179 |
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irk-123456789-1491792019-02-20T01:27:22Z Induced Modules for Affine Lie Algebras Futorny, V. Kashuba, I. We study induced modules of nonzero central charge with arbitrary multiplicities over affine Lie algebras. For a given pseudo parabolic subalgebra P of an affine Lie algebra G, our main result establishes the equivalence between a certain category of P-induced G-modules and the category of weight P-modules with injective action of the central element of G. In particular, the induction functor preserves irreducible modules. If P is a parabolic subalgebra with a finite-dimensional Levi factor then it defines a unique pseudo parabolic subalgebra Pps, P Ì Pps. The structure of P-induced modules in this case is fully determined by the structure of Pps-induced modules. These results generalize similar reductions in particular cases previously considered by V. Futorny, S. König, V. Mazorchuk [Forum Math. 13 (2001), 641-661], B. Cox [Pacific J. Math. 165 (1994), 269-294] and I. Dimitrov, V. Futorny, I. Penkov [Comm. Math. Phys. 250 (2004), 47-63]. 2009 Article Induced Modules for Affine Lie Algebras / V. Futorny, I. Kashuba // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 22 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 17B65; 17B67 http://dspace.nbuv.gov.ua/handle/123456789/149179 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
We study induced modules of nonzero central charge with arbitrary multiplicities over affine Lie algebras. For a given pseudo parabolic subalgebra P of an affine Lie algebra G, our main result establishes the equivalence between a certain category of P-induced G-modules and the category of weight P-modules with injective action of the central element of G. In particular, the induction functor preserves irreducible modules. If P is a parabolic subalgebra with a finite-dimensional Levi factor then it defines a unique pseudo parabolic subalgebra Pps, P Ì Pps. The structure of P-induced modules in this case is fully determined by the structure of Pps-induced modules. These results generalize similar reductions in particular cases previously considered by V. Futorny, S. König, V. Mazorchuk [Forum Math. 13 (2001), 641-661], B. Cox [Pacific J. Math. 165 (1994), 269-294] and I. Dimitrov, V. Futorny, I. Penkov [Comm. Math. Phys. 250 (2004), 47-63]. |
| format |
Article |
| author |
Futorny, V. Kashuba, I. |
| spellingShingle |
Futorny, V. Kashuba, I. Induced Modules for Affine Lie Algebras Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Futorny, V. Kashuba, I. |
| author_sort |
Futorny, V. |
| title |
Induced Modules for Affine Lie Algebras |
| title_short |
Induced Modules for Affine Lie Algebras |
| title_full |
Induced Modules for Affine Lie Algebras |
| title_fullStr |
Induced Modules for Affine Lie Algebras |
| title_full_unstemmed |
Induced Modules for Affine Lie Algebras |
| title_sort |
induced modules for affine lie algebras |
| publisher |
Інститут математики НАН України |
| publishDate |
2009 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/149179 |
| citation_txt |
Induced Modules for Affine Lie Algebras / V. Futorny, I. Kashuba // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 22 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT futornyv inducedmodulesforaffineliealgebras AT kashubai inducedmodulesforaffineliealgebras |
| first_indexed |
2023-05-20T17:32:31Z |
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2023-05-20T17:32:31Z |
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1796153528455004160 |