Geometries, the principle of duality, and algebraic groups

Details Geometries, the principle of duality, and algebraic groups Geometries, the principle of duality, and algebraic groups

2005-03-10

arxiv.org/abs/math/0503201v2

Expositiones Mathematicae 24 #3 (2006), 195-234

Mathematics

Representation Theory

The writing has been cleaned up since v1

Scientific paper

10.1016/j.exmath.2005.11.001

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.

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