Parabolic subgroups and automorphism groups of Schubert varieties

Automorphism Groups of 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.

Parabolic subgroups of Garside groups

A Garside monoid is a cancellative monoid with a finite lattice generating set; a Garside group is the group of fractions of a Garside monoid. The family of Garside groups contains the Artin-Tits groups of spherical type. We generalise the well-known notion of a parabolic subgroup of an Artin-Tits group into that of a parabolic subgroup of a Garside group. We also define the more general notion...

On Automorphism Groups of Parabolic Geometries

Jordan Groups and Automorphism Groups of Algebraic Varieties

The first section of this paper is focused on Jordan groups in abstract setting, the second on that in the settings of automorphisms groups and groups of birational self-maps of algebraic varieties. The appendix contains formulations of some open problems and the relevant comments. MSC 2010: 20E07, 14E07