Representation Theory: Home Page

Example sheets, solution sheets and other material related to the course will be posted here.

Example Sheet 1 (PDF file). Questions 2,3,4 were set on Friday 9th October.
- Solutions 1.
Example Sheet 2 (PDF file). Questions 1, 4 were set on Monday 19th October.
- Solutions 2.
Example Sheet 3 (PDF file). Questions 3,5 were set on Friday 23rd October.
- Solutions 3.
Example Sheet 4 (PDF file). Questions 3,5,6 were set on Monday 2nd November.
- Solutions 4.
Example Sheet 5 (PDF file). Questions 2,5 were set on Friday 6th November.
- Solutions 5.
Example Sheet 6 (PDF file). Questions 1,3,4 were set on Friday 13th November.
- Solutions 6.
Example Sheet 7 (PDF file). Questions 1,3,4 were set on Friday 20th November.
- Solutions 7.
Example Sheet 8 (PDF file). Questions 1,3 were set on Friday 27th November.
- Solutions 8.
Example Sheet 9 (PDF file). Question 1 was set on Friday 4th December.
- Solutions 9.
Example Sheet 10 (PDF file). Question 1,3 were set on Monday 11th January.

Let f(g) be the number of ways of expressing an element g of a group G as a commutator. Here is a proof of the formula (which I mentioned in lectures) giving the class function f as a linear combination of irreducible characters. Using this formula, the fact that the degree of every irreducible character divides the order of the group is easily seen to be equivalent to the fact that f is a character. Is there a direct way to see that it's a character?