Geometries, the principle of duality, and algebraic groups
Jacques Tits gave a general recipe for producing an abstract
geometry from a semisimple algebraic group. This expository paper describes a
uniform method for giving a concrete realization of Tits's geometry and works
through several examples. We also give a criterion for recognizing the
automorphism of the geometry induced by an automorphism of the group. The
E6 geometry is studied in depth.
(This paper has appeared in Expositiones Mathematicae, vol. 24, No. 3 (2006)
195-234)
M. Carr < mpcarr@umich.edu >
S. Garibaldi < skip@member.ams.org >