Buildings and Classical Groups
This course will be a mix of algebra, a
little number theory, and some elementary facts from topology. It
begins with a discussion of Coxeter groups (generalized reflection
groups), and how, associated to such a group, one can create a
topological object (simplicial complex). Coxeter groups are
characterized by an associated Coxeter diagram, very much analogous to
the Dynkin diagrams one sees in the study of simple Lie algebras.
The course will go back and forth between geometric and algebraic
perspectives, and in the end I hope to talk about some connections of
buildings to number theory, specifically to the theory of Hecke
algebras and modular forms.
The prerequisites are algebra at the level of 101.
Last modified by
T. R. Shemanske on 10 Dec 1998
Graphics by The Gimp