Ground state representations of loop algebras
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2010
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| _version_ | 1866911340135710720 |
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| author | Tanimoto, Yoh |
| author_facet | Tanimoto, Yoh |
| contents | Let g be a simple Lie algebra, Lg be the loop algebra of g. Fixing a point in S^1 and identifying the real line with the punctured circle, we consider the subalgebra Sg of Lg of rapidly decreasing elements on R. We classify the translation-invariant 2-cocycles on Sg. We show that the ground state representation of Sg is unique for each cocycle. These ground states correspond precisely to the vacuum representations of Lg. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1005_0270 |
| institution | arXiv |
| publishDate | 2010 |
| record_format | arxiv |
| spellingShingle | Ground state representations of loop algebras Tanimoto, Yoh Representation Theory Mathematical Physics 81R10(primary), 22E67, 81R15(secondary) Let g be a simple Lie algebra, Lg be the loop algebra of g. Fixing a point in S^1 and identifying the real line with the punctured circle, we consider the subalgebra Sg of Lg of rapidly decreasing elements on R. We classify the translation-invariant 2-cocycles on Sg. We show that the ground state representation of Sg is unique for each cocycle. These ground states correspond precisely to the vacuum representations of Lg. |
| title | Ground state representations of loop algebras |
| topic | Representation Theory Mathematical Physics 81R10(primary), 22E67, 81R15(secondary) |
| url | https://arxiv.org/abs/1005.0270 |