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 .

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#
group representations

# Faithful representations and tensor products

# Be rational

# Fundamental theorem of algebra…?

# Some representation theory

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 .

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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 .