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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2009 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2009
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/149179 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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| _version_ | 1862714600488697856 |
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| author | Futorny, V. Kashuba, I. |
| author_facet | Futorny, V. Kashuba, I. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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].
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| first_indexed | 2025-12-07T17:51:53Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-149179 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T17:51:53Z |
| publishDate | 2009 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Futorny, V. Kashuba, I. 2019-02-19T18:14:16Z 2019-02-19T18:14:16Z 2009 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 https://nasplib.isofts.kiev.ua/handle/123456789/149179 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]. This paper is a contribution to the Special Issue on Kac–Moody Algebras and Applications. The first author is supported in part by the CNPq grant (301743/2007-0) and by the Fapesp grant (2005/60337-2). The second author is supported by the Fapesp grant (2007/025861). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Induced Modules for Affine Lie Algebras Article published earlier |
| spellingShingle | Induced Modules for Affine Lie Algebras Futorny, V. Kashuba, I. |
| title | 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_short | Induced Modules for Affine Lie Algebras |
| title_sort | induced modules for affine lie algebras |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149179 |
| work_keys_str_mv | AT futornyv inducedmodulesforaffineliealgebras AT kashubai inducedmodulesforaffineliealgebras |