Instructor: |
Monty (or William)
McGovern
Office: Padelford C-450 Phone: 206-543-1149 Email: mcgovern@math.washington.edu Office Hours: TTh 10:30 and by appointment |
Lectures: |
Monday, Wednesday & Friday, 10:30-11:20 p.m., Smith Hall 111 |
Required Text: |
Reflection Groups and Coxeter Groups by James Humphreys (Cambridge, 1990) |
Prerequisites: |
to be in the good graces of the instructor |
Incompletes and Drops: |
The grade of Incomplete will be given ONLY if a student has been doing satisfactory work until the end of the quarter and then misses the final exam for a documented illness, religious reason, or family emergency. |
What to Expect: |
This course is the first of a two-quarter sequence. In the first quarter we will cover most of Chapters 1-3 and 7 in Humphreys, covering the basic properties and classification of finite reflection groups, invariant theory of these groups, and an introduction to Kazhdan-Lusztig theory. The second quarter will be taught by Professor Sara Billey and will cover some of the remaining chapters, together with some related topics from her research. |
Due: | Problems: |
Jan 7 |
Exercises 1.1.2,1.3.1,1.3.2; show that no finite-dimensional
real vector space is a finite union of proper subspaces; read sections 1.1--1.6 |
Jan 14 |
Exercises 1.5.1,2,3,1.6.1: read sections 1.7--1.9 |
Jan 21 |
Exercises 2.2.1,2.8.1,2.10.1,2.11.1: read section 1.12 and Chapter 2
|
Jan 28
|
Construct algebraically independent generators of R in the
classical and dihedral cases, WITHOUT peeking at the book: read
3.1--3.10 |
Feb 4 |
Compute the Jacobians of the basic invariants in the classical
cases: read the rest of Chapter 3 |
Feb 11 |
read sections 4.1--4.3 |
Feb 18 |
Look up the formula for the order of the orthogonal group over a
finite field of odd order: read the rest of Chapter 4 |
Feb 28
|
7.3.1,2: read 7.1--7.9 |
Mar 4
|
Compute the Kazhdan-Lusztig and R-polynomials for dihedral
groups: read 7.11--7.15 |
Mar 11
|
read your favorite book |