3-4 hours of lectures per week.
Lecturer
Henning Haahr Andersen
Content
The symmetric groups Sn from Algebra 1 are the rst examples of Coxeter groups. We shall in this course more generally introduce reection groups and study their basic properties. For instance, we shall show that they possess a length function, that their elements have reduced expressions, and that these satisfy the exchange condition. Then we shall give the general definition of Coxeter groups. Such groups occur in several branches of mathematics. We shall mostly concentrate on aspects related to representation theory.
In the second half of the course we introduce Hecke algebras. These algebras are closely related to Coxeter groups and it is easy to give a number of concrete examples. We shall study the famous Kazhdan-Lusztig polynomials which show up in relation to a certain canonical basis for the Hecke algebra.
Prerequisites
Algebra 2 (e.g. followed simultaneously) or Representation Theory.
Literature
J. E. Humphreys, Reection groups and Coxeter groups, Cambridge studies in advanced mathematics 29, Cambridge University Press 1990.
Evaluation
Students who do not intend to take a degree in Mathematics or Statistics from the University of Aarhus, but wish to earn credits for a 2.dels course from the Department of Mathematics, should indicate at the beginning of the course that they wish to be examined.
The form of examination for these students will be active participation together with oral or written contributions.
Credits
10 ECTS
Semester
Spring 2003