Coxeter groups are studied using mainly combinatorial techniques, although connections with other areas will be prevalent. This is a thriving field of research and recent results will be touched upon.
FSF3701 Coxeter Groups 7.5 credits
This course has been discontinued.
Decision to discontinue this course:
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Information per course offering
Course offerings are missing for current or upcoming semesters.
Course syllabus as PDF
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Course syllabus FSF3701 (Spring 2019–)Headings with content from the Course syllabus FSF3701 (Spring 2019–) are denoted with an asterisk ( )
Content and learning outcomes
Course contents
Intended learning outcomes
The theory of Coxeter groups provides a common framework for important classes of groups such as symmetric groups, Weyl groups, reflections groups (finite, affine, hyperbolic) and symmetry groups of regular polytopes.
After passing the course the students will understand, and are able to apply, the theory in Lie theory, algebraic geometry and combinatorial geometry among other subjects
Literature and preparations
Specific prerequisites
A Master degree including at least 30 university credits (hp) in in Mathematics.
Literature
A. Björner and F. Brenti, Combinatorics of Coxeter groups, Graduate Texts in Mathematics 231, Springer, New York, 2005.
J. E. Humphreys, Reflection groups and Coxeter groups, Cambridge studies in advanced mathematics 29, Cambridge University Press, 1990.
Examination and completion
Grading scale
P, F
Examination
- INL1 - Assignment, 7.5 credits, grading scale: P, F
Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.
The examiner may apply another examination format when re-examining individual students.
If the course is discontinued, students may request to be examined during the following two academic years.
Homework, possibly combined with some seminar/oral assignment.
Other requirements for final grade
Accepted homework and oral presentations.
Examiner
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Ethical approach
- All members of a group are responsible for the group's work.
- In any assessment, every student shall honestly disclose any help received and sources used.
- In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.
Further information
Course room in Canvas
Registered students find further information about the implementation of the course in the course room in Canvas. A link to the course room can be found under the tab Studies in the Personal menu at the start of the course.
Offered by
Education cycle
Third cycle