Automorphism Groups of Parabolic Geometriesandreas

Spaces and Twistor Spacesfor Parabolic Geometriesandreas

Automorphism Groups of Parabolic Geometries

We show that elementary algebraic techniques lead to surprising results on automorphism groups of Cartan geometries and especially parabolic geometries. The example of three–dimensional CR structures is discussed in detail.

On Automorphism Groups of Parabolic Geometries

Automorphisms of nearly finite Coxeter groups

Suppose that W is an infinite Coxeter group of finite rank n, and suppose that W has a finite parabolic subgroup WJ of rank n 1. Suppose also that the Coxeter diagram of W has no edges with infinite labels. Then any automorphism of W that preserves reflections lies in the subgroup of AutðWÞ generated by the inner automorphisms and the automorphisms induced by symmetries of the Coxeter graph. If...

On Automorphism Groups of Some Types of Generic Distributions

To certain types of generic distributions (subbundles in a tangent bundle) one can associate canonical Cartan connections. Many of these constructions fall into the class of parabolic geometries. The aim of this article is to show how strong restrictions on the possibles sizes of automorphism groups of such distributions can be deduced from the existence of canonical Cartan connections. This ne...