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.

TEXTBOOK

Anders Björner and Francesco Brenti,COURSE OUTLINE

- Introduction.
- Bruhat order.
- Weak order and reduced words.
- Root systems, games and automata.
- Combinatorial descriptions.
- Enumeration.
- Kazhdan-Lusztig and R-polynomials.
- Other material, as time permits.

PREQUISITE: There is no formal prerequisite for this course. Knowledge of algebra or combinatorics is useful, but not necessary.

http://www.math.uky.edu/~readdy/714/Coxeter_Groups/