Automorphisms of generalised polygons
James Parkinson (University of Sydney)
Thursday 5th September, 2013 16:00-17:00 Maths 516
In this talk we investigate the combinatorial interplay between automorphisms and opposition in (primarily finite) generalised polygons. Our main aim is to provide some restrictions on how an arbitrary automorphism of a generalised polygon can act, particularly with respect to the opposition relation. In this direction, we give a precise description of the fixed element structures of automorphisms of a generalised polygon mapping no chamber to an opposite chamber, and we give a complete classification of automorphisms of finite generalised polygons which map at least one point and at least on line to an opposite, but map no chamber to an opposite chamber. One motivation for this investigation is towards the important conjectures surrounding the classification of flag-transitive finite polygons.
This is joint work with Beukje Temmermans and Hendrik Van Maldeghem.