Summer School on Algebraic and Enumerative Combinatorics
Lectures by Francesco Brenti
S. Miguel de Seide, Portugal
Topic: Combinatorics of Coxeter Groups
- Coxeter systems.
- Length function.
- The geometric representation.
- Root systems.
- Parabolic subgroups and quotients.
- Geometric interpretation of the length function.
- Roots and reflections.
- The exchange condition.
- Bruhat order.
- Reduced expressions and subexpressions.
- Irreducible systems.
- The classification theorem.
- Hecke algebras.
- R-polynomials.
- Kazhdan-Lusztig polynomials.
Suggested reading
- A. Bjorner, F. Brenti, "Combinatorics of Coxeter Groups",
Graduate Texts in Mathematics, 231, Springer-Verlag, New York, 2005. (Chapter 2)
- J. E. Humphreys, "Reflection Groups and Coxeter Groups",
Cambridge Studies in Advanced Mathematics, 29,
Cambridge Univ. Press, Cambridge, 1990.
(Chapter 5)