- 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!