## Lie Groups Homework Solutions -- Spring
2006

Homework is due on Thursdays 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. Solutions in pdf
or postscript

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. Solutions in pdf
or postscript

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. Solutions in pdf or postscript.

HW 4 (due TUESDAY, February 28) Section 2.5, problems 2, 5, 7,
11, 12; Section 2.6, problems 6, 7, 8. Solutions in pdf or postscript.

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. Solutions in pdf
or postscript.

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. Solutions in pdf or postscript.

HW7 (due THURSDAY, April 6) Section 4.2, problems 6, 9, 10.
Section 4.3, problems 5, 6. Solutions in pdf
or postscript.

HW8 (due TUESDAY, April 18) Section 5.2, problems 2,3.
Section 5.3, problems 2,3. Solutions in pdf
or postscript.