mathfrak{k}$-structure of basic representation of affine algebras
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...
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| Main Author | |
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| Format | Journal Article |
| Language | English |
| Published |
17.07.2024
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| Subjects | |
| Online Access | Get full text |
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| Summary: | 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. |
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| DOI: | 10.48550/arxiv.2407.12748 |