Generalized spin representations

Hainke, Guntram and Koehl, Ralf and Levy, Paul (2015) Generalized spin representations. Muenster Journal of Mathematics. ISSN 1867-5778

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We introduce the notion of a generalized spin representation of the maximal compact subalgebra $\mathfrak k$ of a symmetrizable Kac--Moody algebra $\mathfrak g$ in order to show that, if defined over a formally real field, every such $\mathfrak k$ has a non-trivial reductive finite-dimensional quotient. The appendix illustrates how to compute the isomorphism types of these quotients for the real $E_n$ series. In passing this provides an elementary way of determining the isomorphism types of the maximal compact subalgebras of the semisimple split real Lie algebras of types $E_6$, $E_7$, $E_8$.

Item Type: Journal Article
Journal or Publication Title: Muenster Journal of Mathematics
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 73877
Deposited By: ep_importer_pure
Deposited On: 31 Jul 2015 10:52
Refereed?: Yes
Published?: Published
Last Modified: 19 Feb 2020 02:27

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