- Why are diagonal matrices their own normaliser?
- How you do define determinant for a general linear operator? (i.e without defining a basis)
- Why is the exponential map well defined for matrices? Where the exponential map takes a matrix to its exponential Taylor series.
- Consider , what is , and what is ?
- Show the rank of is n, where rank is the dimension of a Cartan Subalgebra.
- Show that the regular elements in are diagonal matrices with no repeated entries.
- If we define the map which takes a root , For which root systems is this in the Weyl Group?
- (Very optional) Why is the Dynkin diagram for not allowed to have a connection on the central root?
Don’t forget that next week is the problem session!