Harmonic Analysis and Free Field Realization of the Takiff Supergroup of GL(1|1)
Takiff superalgebras are a family of non semi-simple Lie superalgebras that are believed to give rise to a rich structure of indecomposable representations of associated conformal field theories. We consider the Takiff superalgebra of gl(1|1), especially we perform harmonic analysis for the correspo...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2015 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2015
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147138 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Harmonic Analysis and Free Field Realization of the Takiff Supergroup of GL(1|1) / A. Babichenko, T. Creutzig // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 50 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862690602145021952 |
|---|---|
| author | Babichenko, A. Creutzig, T. |
| author_facet | Babichenko, A. Creutzig, T. |
| citation_txt | Harmonic Analysis and Free Field Realization of the Takiff Supergroup of GL(1|1) / A. Babichenko, T. Creutzig // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 50 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Takiff superalgebras are a family of non semi-simple Lie superalgebras that are believed to give rise to a rich structure of indecomposable representations of associated conformal field theories. We consider the Takiff superalgebra of gl(1|1), especially we perform harmonic analysis for the corresponding supergroup. We find that every simple module appears as submodule of an infinite-dimensional indecomposable but reducible module. We lift our results to two free field realizations for the corresponding conformal field theory and construct some modules.
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| first_indexed | 2025-12-07T16:13:51Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-147138 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T16:13:51Z |
| publishDate | 2015 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Babichenko, A. Creutzig, T. 2019-02-13T17:22:42Z 2019-02-13T17:22:42Z 2015 Harmonic Analysis and Free Field Realization of the Takiff Supergroup of GL(1|1) / A. Babichenko, T. Creutzig // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 50 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 17B67; 17B81; 22E46; 81R10; 81T40 DOI:10.3842/SIGMA.2015.067 https://nasplib.isofts.kiev.ua/handle/123456789/147138 Takiff superalgebras are a family of non semi-simple Lie superalgebras that are believed to give rise to a rich structure of indecomposable representations of associated conformal field theories. We consider the Takiff superalgebra of gl(1|1), especially we perform harmonic analysis for the corresponding supergroup. We find that every simple module appears as submodule of an infinite-dimensional indecomposable but reducible module. We lift our results to two free field realizations for the corresponding conformal field theory and construct some modules. A. Babichenko is thankful for hospitality to DESY Hamburg Theory Group and to ETH Zurich
 Institute for Theoretical Physics, where the final part of this work was done. His work was supported
 by SFB676, and his visit to ETH – by Pauli Center for Theoretical Studies. T. Creutzig
 is supported by NSERC Research Grant (Project #: RES0020460). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Harmonic Analysis and Free Field Realization of the Takiff Supergroup of GL(1|1) Article published earlier |
| spellingShingle | Harmonic Analysis and Free Field Realization of the Takiff Supergroup of GL(1|1) Babichenko, A. Creutzig, T. |
| title | Harmonic Analysis and Free Field Realization of the Takiff Supergroup of GL(1|1) |
| title_full | Harmonic Analysis and Free Field Realization of the Takiff Supergroup of GL(1|1) |
| title_fullStr | Harmonic Analysis and Free Field Realization of the Takiff Supergroup of GL(1|1) |
| title_full_unstemmed | Harmonic Analysis and Free Field Realization of the Takiff Supergroup of GL(1|1) |
| title_short | Harmonic Analysis and Free Field Realization of the Takiff Supergroup of GL(1|1) |
| title_sort | harmonic analysis and free field realization of the takiff supergroup of gl(1|1) |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147138 |
| work_keys_str_mv | AT babichenkoa harmonicanalysisandfreefieldrealizationofthetakiffsupergroupofgl11 AT creutzigt harmonicanalysisandfreefieldrealizationofthetakiffsupergroupofgl11 |