## 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.