Coxeter groups arise in nature, whether as symmetry groups of regular polytopes, tesselations of the plane, juggling patterns, or more generally, as reflections. We will look at Coxeter groups from a combinatorial, geometric and algebraic approach.
This course serves both as an introduction to Coxeter groups and a glimpse into the current research trends, including combinatorial descriptions of finite and affine Weyl groups, the complete cd-index and Kazhdan-Lusztig polynomials.
We will be following Björner and Brenti's recent book on Coxeter groups. We will also be reading some recent papers in the field.
TEXTBOOKAnders Björner and Francesco Brenti, Combinatorics of Coxeter Groups, Springer, 2005.