(\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 representa...

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Bibliographic Details
Published inarXiv.org
Main Author König, Benedikt
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 17.07.2024
Subjects
Representations
Supergravity
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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.
ISSN:2331-8422