University of Sydney Algebra Seminar

James Parkinson (University of Sydney)

Friday 28th March, 12:05-12:55pm, Place: 373

Automorphisms of generalised polygons

Generalised polygons are basic graphs that play an important role in Lie theory, being the atomic building blocks of higher geometries called buildings. In this talk we report on recent joint work with Hendrik Van Maldeghem (Ghent) concerning automorphisms of (primarily finite) generalised polygons, focusing on the interplay between the automorphism and the opposition relation in the polygon. This includes the complete classification of so called `exceptional domestic' automorphisms of finite generalised polygons, and a detailed investigation of `anisotropic' automorphisms. One motivation for this study is towards the old conjectures of Kantor surrounding the classification of flag-transitive finite polygons.