Reflection groups and their generalisations, Coxeter systems, permutation representations,
reduced words, Bruhat order, Kazhdan-Lusztig theory, Chevalley’s theorem, Poincare series,
root systems, classification of finite and affine Coxeter groups
No prior knowledge of combinatorics or algebra is expected, but we will assume a
familiarity with linear algebra and basics of group theory.
Suggested books and references:
Anders Bjorner & Francesco Brenti, Combinatorics of Coxeter Groups, Springer GTM, 2005.
James E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge University Press, 1990.
Michael W. Davis, The Geometry and Topology of Coxeter Groups, Princeton University Press, 2008.
Nicolas Bourbaki, Elements Of Mathematics: Lie Groups and Lie Algebras: Chapters 4-6, Springer 2002.