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Harmonic Analysis and Free Field Realization of the Takiff Supergroup of GL(1|1)
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2015, том 11
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Harmonic Analysis and Free Field Realization of the Takiff Supergroup of GL(1|1)
Інший ID:
2010 Mathematics Subject Classification: 17B67; 17B81; 22E46; 81R10; 81T40
DOI:10.3842/SIGMA.2015.067
DOI:10.3842/SIGMA.2015.067
Посилання:
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.
Підтримка:
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).
Дата:
2015
Переглядів:
565
Завантажень:
223
Анотація:
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.
