give an orthonormal basis for the -module . give the matrix of the generators and in the corresponding representation, and give the branching rule for in this case.
ok. so I know that has basis , that is a -module if linearity and bracket preservation hold, and I know that
because the basis of has 9 elements, does that mean that the orthonormal basis for the -module will also have 9 elements? and does ? im also a little confused as to what the -module actually is...any help AT ALL will be greatly appreciated!