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k-structure of basic representation of affine algebras

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König,  Benedikt
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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2407.12748.pdf
(Preprint), 706KB

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Citation

König, B. (in preparation). k-structure of basic representation of affine algebras.


Cite as: https://hdl.handle.net/21.11116/0000-000F-DC20-5
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.