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arXiv · 2407.12748

$\mathfrak{k}$-structure of basic representation of affine algebras

Benedikt König
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Abstract

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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Benedikt König. 2024-07-17. $\mathfrak{k}$-structure of basic representation of affine algebras. https://arxiv.org/abs/2407.12748

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