Generalized spin representations

Abstract

We introduce the notion of a generalized spin representation of the maximal compact subalgebra of a symmetrizable Kac-Moody algebra in order to show that, if defined over a formally real field, every such subalgebra 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 $E_6$, $E_7$, $E_8$.

merged arXiv:1403.4463 into this document as an appendix

References in corpus (5)

• On higher spin realizations of K(E10)
• On Deformations and Contractions of Lie Algebras
• Kac-Moody Algebras in M-theory
• On topological twin buildings and topological split Kac-Moody groups
• Exceptional Lie algebras and M-theory

Cited by in corpus (5)

• Kac-Moody symmetric spaces
• A Lightcone Embedding of the Twin Building of a Hyperbolic Kac-Moody Group
• Generalized spin representations. Part 2: Cartan-Bott periodicity for the split real En series
• Orthogonal forms of Kac--Moody groups are acylindrically hyperbolic
• Representations of Quantum Minimal Surface Algebrasvia Kac-Moody-theory