Generalized spin representations. Part 2: Cartan-Bott periodicity for the split real En series
Rings and Algebras
2014-03-19 v1 Representation Theory
Abstract
In this article we analyze the quotients of the maximal compact subalgebras of the split real Kac-Moody algebras of the En series resulting from the generalized spin representations introduced in part 1. It turns out that these quotients satisfy a Cartan-Bott periodicity. Our findings are also meaningful in the finite-dimensional cases of A2 + A1, A4, D5, E6, E7, E8, where it turns out that the generalized spin representation is injective. Consequently the observed Cartan-Bott periodicity provides a structural explanation for the seemingly sporadic isomorphism types of the maximal compact Lie subalgebras of the split real Lie algebras of types E6, E7, E8.
Keywords
Cite
@article{arxiv.1403.4463,
title = {Generalized spin representations. Part 2: Cartan-Bott periodicity for the split real En series},
author = {Max Horn and Ralf Köhl},
journal= {arXiv preprint arXiv:1403.4463},
year = {2014}
}