$\mathfrak{k}$-structure of basic representation of affine algebras
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911958801842176 |
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| author | König, Benedikt |
| author_facet | König, Benedikt |
| contents | This article presents a new relation between the basic representation of split real simply-laced affine Kac-Moody algebras and finite dimensional representations of its maximal compact subalgebra $\mathfrak{k}$. We provide infinitely many $\mathfrak{k}$-subrepresentations of the basic representation and we prove that these are all the finite dimensional $\mathfrak{k}$-subrepresentations of the basic representation such that the quotient of the basic representation by the subrepresentation is a finite dimensional representation of a certain parabolic algebra and of the maximal compact subalgebra. By this result we provide an infinite composition series with a cosocle filtration of the basic representation. Finally, we present examples of the results and applications to supergravity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_12748 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $\mathfrak{k}$-structure of basic representation of affine algebras König, Benedikt Representation Theory High Energy Physics - Theory This article presents a new relation between the basic representation of split real simply-laced affine Kac-Moody algebras and finite dimensional representations of its maximal compact subalgebra $\mathfrak{k}$. We provide infinitely many $\mathfrak{k}$-subrepresentations of the basic representation and we prove that these are all the finite dimensional $\mathfrak{k}$-subrepresentations of the basic representation such that the quotient of the basic representation by the subrepresentation is a finite dimensional representation of a certain parabolic algebra and of the maximal compact subalgebra. By this result we provide an infinite composition series with a cosocle filtration of the basic representation. Finally, we present examples of the results and applications to supergravity. |
| title | $\mathfrak{k}$-structure of basic representation of affine algebras |
| topic | Representation Theory High Energy Physics - Theory |
| url | https://arxiv.org/abs/2407.12748 |