Geometry of one-tori
Nikolai Vavilov (University of Saint-Petersburg and Queen's Univers)
Monday 28th January, 2008 16:00-17:00 214, Mathematics Building
The ``geometries'' we talk about are combinatorial geometries in the style of Tits and Buekenhout. In the 1950's Tits noticed that many geometric properties of algebraic groups can be expressed in internal group-theoretical terms, the key concept being that of parabolic subgroup. Little is known about such geometries defined in terms of semi-simple elements/tori. Until recently the only example that was well understood, was the toy case of 1-tori, i.e., reflection tori in GL_n, studied by the author, Cohen, Cuypers and Sterk. I will show that if a subgroup $H$ of a Chevalley group contains a small semi-simple element, and the field is not too small, then $H$ contains small unipotent elements.