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EnglishThe real compact supergroup S^1|1 is analysed from different perspectives and its representation theory is studied. We prove it is the only (up to isomorphism) supergroup, which is a real form of (C1|1)× with reduced Lie group S^1, and a link with SUSY structures on C^1|1 is established. We describe a large family of complex semisimple representations of S^1|1 and we show that any S^1|1-representation whose weights are all nonzero is a direct sum of members of our family. We also compute the matrix elements of the members of this family and we give a proof of the Peter-Weyl theorem for S^1|1
SUSY structures, representations and Peter-Weyl theorem for S<sup>1|1</sup> / Carmeli, C.; Fioresi, R; Kwok, S.. - In: JOURNAL OF GEOMETRY AND PHYSICS. - ISSN 0393-0440. - STAMPA. - 95(2015), pp. 144-158.
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| Titolo: | SUSY structures, representations and Peter-Weyl theorem for S<sup>1|1</sup> |
| Autori: | |
| Data di pubblicazione: | 2015 |
| Rivista: | |
| Citazione: | SUSY structures, representations and Peter-Weyl theorem for S<sup>1|1</sup> / Carmeli, C.; Fioresi, R; Kwok, S.. - In: JOURNAL OF GEOMETRY AND PHYSICS. - ISSN 0393-0440. - STAMPA. - 95(2015), pp. 144-158. |
| Abstract: | The real compact supergroup S^1|1 is analysed from different perspectives and its representation theory is studied. We prove it is the only (up to isomorphism) supergroup, which is a real form of (C1|1)× with reduced Lie group S^1, and a link with SUSY structures on C^1|1 is established. We describe a large family of complex semisimple representations of S^1|1 and we show that any S^1|1-representation whose weights are all nonzero is a direct sum of members of our family. We also compute the matrix elements of the members of this family and we give a proof of the Peter-Weyl theorem for S^1|1 |
| Handle: | http://hdl.handle.net/11567/856821 |
| Appare nelle tipologie: | 01.01 - Articolo su rivista |
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