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
Автори: Futorny, V., Kashuba, I.
Формат: Стаття
Мова:English
Опубліковано: Інститут математики НАН України 2009
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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spelling 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
last_indexed 2023-05-20T17:32:31Z
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