MATH6032  Topics in Algebra II  2022/23
General Information
Lecturer

Felix Schremmer
 Office: LSB232A
 Tel: 39437978
 Email:
Time and Venue
 Lecture: Wednesday 9:3012:15, LSB219
Course Description
By definition, a reflection group is a subgroup of the orthogonal group which is generated by a finite set of reflections. The concept of a Coxeter group is a purely grouptheoretic analogue of those reflection groups. While the definition of a Coxeter group is fairly accessible, as it is a finitely presented group of a very specific shape, the theory is rather deep and still subject to research.
Typical examples of Coxeter groups are dihedral groups and symmetric groups. While the most important application of Coxeter groups is definitely Lie theory (coming from Weyl groups and affine Weyl groups), the theory is also relevant for classical geometry and knot theory.
The course will be divided into two parts. The first part will cover the fundamental structure theory of Coxeter groups, such as Bruhat order and parabolic subgroups. In the second part, we will turn our attention to more advanced topics related to Coxeter groups, depending on the participants' interests and backgrounds.
Textbooks
 Andreas Björner, Francesco Brenti: Combinatorics of Coxeter Groups
 James Humphreys: Reflection groups and Coxeter groups
 Nicholas Bourbaki: Groupes et algèbres de Lie
 Cédric Bonnafé: KazhdanLusztig Cells with Unequal Parameters
Lecture Notes
Class Notes
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Assessment Policy Last updated: March 22, 2023 09:18:56