Point-line geometries related to (exceptional) spherical buildings

Anneleen De Schepper (Ghent)

Abstract

In the 70'ies, Cooperstein introduced "parapolar spaces", certain point-line geometries, to axiomatically capture the Grassmannians associated to (exceptional) spherical buildings, which at their turn serve as a geometric interpretation to semisimple algebraic groups. Apart from point and lines, parapolar spaces consist of projective spaces and polar spaces. In contrast to these well-understood substructures, and although most known examples of parapolar spaces are related to buildings indeed, there is no general classification. I intend to give a gentle introduction to parapolar spaces and their relation to buildings and at the end I will discuss some partial classification results.