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General


Description

Let V be a Euclidean space. The finite reflection groups on V play a central role in the study of finite groups and of algebraic groups. We shall begin by classifying all the finite subgroup of the orthogonal group O(V) when V has dimension 2 or 3. For G a finite subgroup of O(V), we then introduce fundamental regions for the action of G on V. Following this we define Coxeter groups as finite groups generated by reflections in O(V) which act effectively on V. To study such subgroups of O(V) we introduce root systems and show that G simply transitively on the positive systems in the root system. In the final chapter, we classify root systems and thus also classify the Coxeter groups. This classification is as usual parameterized by the Coxeter diagrams. This classification is as usual parameterized by the Coxeter diagrams. As time allows I will cover further material. This will be chosen from: Presentations of Coxeter Groups, Invariants of Coxeter Groups, Affine Reflection groups, Complex reflection groups.

Semester

Spring 2010 (Monday, January 11 to Friday, March 19)

Timetable

  • Mon 11:05 - 11:55
  • Fri 11:05 - 11:55

Prerequisites

No prerequisites information is available yet.

Syllabus

No syllabus information is available yet.

Lecturer


Christopher Parker
Email c.w.parker@bham.ac.uk
Phone (0121) 414 6199
Interests Finite groups
Photo of Christopher Parker


Students


Photo of PEDEN Andrew
PEDEN Andrew
(Leicester)
Photo of Heather BURKE
Heather BURKE
(Leeds)
Photo of Tim Crinion
Tim Crinion
(Manchester)
Photo of Asma Ismail
Asma Ismail
(Exeter)
Photo of Anton Izosimov
Anton Izosimov
(Loughborough)
Photo of Daniel Kirk
Daniel Kirk
(Leeds)
Photo of Parsons Mark
Parsons Mark
(Reading)
Photo of John McLeod
John McLeod
(Durham)
Photo of Athirah MohamedNawawi
Athirah MohamedNawawi
(Manchester)
Photo of Andrew Monaghan
Andrew Monaghan
(Liverpool)
Photo of Yann Palu
Yann Palu
(Leeds)
Photo of Heather Riley
Heather Riley
(Manchester)


Bibliography


No bibliography has been specified for this course.

Assessment



No assessment information is available yet.

No assignments have been set for this course.

Files


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Week(s)File
Finite Reflection Groups2.pdf


Recorded Lectures


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