Summary: Seminar in Algebra and Number Theory Reflection Groups and Hecke Algebras
Fall 2005 P. Achar
Professor: Pramod N. Achar
Office: 266 Lockett Hall
Office hours: Tues. 10:30am12:00pm
If you cannot make it to my office hours, you may arrange to meet with me at another time by appointment.
Textbook. For much of the semester, we will be working from the book
J. E. Humphreys, Reflection groups and Coxeter groups, Cambridge Advanced Studies in Mathematics,
no. 29, Cambridge University Press, Cambridge, 1990.
However, Humphreys does not cover as much material on Hecke algebras as I would like. A good reference
for additional material on Hecke algebras is:
M. Geck and G. Pfeiffer, Characters of finite Coxeter groups and Iwahori-Hecke algebras, London Mathe-
matical Society Monographs, New Series, no. 21, Oxford University Press, New York, 2000.
It is not necessary to buy the Geck-Pfeiffer book.
Course outline. A tentative list of topics for the semester is as follows:
Real reflection groups, Coxeter groups (Humphreys, Chap. 1, 2, 5) 3 weeks
Polynomial invariants (Humphreys, Chap. 3) 1 week