Lie Groups Homework
Assignments -- Spring 2006
Homework is due at the beginning of class. Depending on
the
length of the assignment, some or all of the problems may be graded.
HW 1 (due January 26): Section 1.1, problems 4, 6; Section
1.2, problems 1, 2, 4.
HW2 (due TUESDAY February 7) : Section 1.3, problems 5,6,7;
Section 2.1,
problems 5, 6, (You do NOT have to do problem 7 on page 43 -- this
problem set turned out harder than originally intended, so we're
skipping that one). Also, don't get too hung up on problem 5 of
section 1.3. It's a little tricky. If you get stuck, assume
the result and attack problems 6 and 7. For problem 5(b) on
page 42, don't try to solve for alpha by hand. Think about
properties of (anti)Hermitian
matrices.
HW3 (due THURSDAY February 16) Section 2.2, problems 1, 3, 4, 8;
Section 2.3, problems 9, 10. Look at (but do not turn in)
Section 2.3, problems 5, 8
HW 4 (due TUESDAY, February 28) Section 2.5, problems 2, 5, 7,
11, 12; Section 2.6, problems 6, 7, 8
HW5 (due THURSDAY, March 9) Section 3.1, problems 1, 6, 11,
12. Section 3.2, problem 6. Also, look at (but do not turn
in) Section 3.1, problem 13.
HW6 (due TUESDAY, March 28). Section 3.2, problem 9.
Section 3.3, problems 1-9. The problems that say "verify"
(namely problems 1, 2, 3, 4, 5 and 9 of section 3.3) do not need to be
turned in, but you SHOULD verify all of these facts to your own
satisfaction. And you DO need to turn in problems 3.2.9,
3.3.6, 3.3.7 and 3.3.8! This problem set builds up the machinery
of root systems.
HW7 (due THURSDAY, April 6) Section 4.2, problems 6, 9, 10.
Section 4.3, problems 5, 6
HW 8 (due TUESDAY, April 18) Section 5.2, problems 2, 3 (part (b) this
gives an example where a right-invariant measure is NOT
left-invariant), 10, Section 5.3 problems 2,3
THERE IS NO HW9. Go ahead and work on your termpapers
instead. If you're looking for extra problems to work for your
own education, I recommend:
Section 6.1, problems 6, 7, 8 and 11, Section 6.2, problems 1 and 2,
Section 6.3, problems 1 and 6, Section 6.4, problems 1 and 2.