Let be a finite group (or a compact Lie group). Prove that if is a faithful finite dimensional complex representation of then any irreducible representation embeds in some tensor product of .
Most of representation theory results work out for algebraically closed fields. For instance, we can classify irreducible representations for the dihedral group with elements over . Classify all irreducible representations for over .
Let be the cyclic group of order and consider the group algebra. Prove that the number of solutions to the equation for is for .
Find all representations over of the group of matrices
where and are in .