Connected subgroups of SO(2,n) acting irreducibly on ${\mathbb{R}}^{2,n}$

Abstract

We classify all connected subgroups of SO(2,n) that act irreducibly on ${\mathbb{R}}^{2,n}$. Apart from $S{O}_0(2,n)$ itself these are $U(1,n/2)$, $SU(1,n/2)$, if $n$ even, $S^1\cdot SO(1,n/2)$ if $n$ even and $n\ge 2$, and $S{O}_0(1,2)$ for $n=3$. Our proof is based on the Karpelevich Theorem and uses the classification of totally geodesic submanifolds of complex hyperbolic space and of the Lie ball. As an application we obtain a list of possible irreducible holonomy groups of Lorentzian conformal structures, namely $S{O}_0(2,n)$, SU(1,n), and $S{O}_0(1,2)$.

22 pages, no figures

References in corpus (1)

• Differential equations and conformal structures