A Lightcone Embedding of the Twin Building of a Hyperbolic Kac-Moody Group
Group Theory, Representation Theory
The twin building of a Kac–Moody group G encodes the parabolic subgroup structure of G and admits a natural G–action. When G is a complex Kac–Moody group of hyperbolic type, we construct an embedding of the twin building of G into the lightcone of the compact real form of the corresponding Kac–Moody algebra. When G has rank 2, we construct an embedding of the spherical building at infinity into the set of rays on the boundary of the lightcone.
Carbone, L., Feingold, A., & Freyn, W. (2016). A lightcone embedding of the twin building of a hyperbolic Kac-Moody group. arXiv preprint arXiv:1606.05638.