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arXiv · 2102.00870

Representations of involutory subalgebras of affine Kac-Moody algebras

Axel Kleinschmidt·Ralf Köhl·Robin Lautenbacher·Hermann Nicolai
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Abstract

We consider the subalgebras of split real, non-twisted affine Kac-Moody Lie algebras that are fixed by the Chevalley involution. These infinite-dimensional Lie algebras are not of Kac-Moody type and admit finite-dimensional unfaithful representations. We exhibit a formulation of these algebras in terms of $\mathbb{N}$-graded Lie algebras that allows the construction of a large class of representations using the techniques of induced representations. We study how these representations relate to previously established spinor representations as they arise in the theory of supergravity.

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Axel Kleinschmidt, Ralf Köhl, Robin Lautenbacher, Hermann Nicolai. 2021-02-01. Representations of involutory subalgebras of affine Kac-Moody algebras. https://doi.org/10.1007/s00220-022-04342-9

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