A Short Proof of Gamas's Theorem

Abstract

If χ^λis the irreducible character of the symmetric group S_n corresponding to the partition λof n then we may symmetrize a tensor v_1 \otimes ... \otimes v_n by χ^λ. Gamas's theorem states that the result is not zero if and only if we can partition the set {v_i} into linearly independent sets whose sizes are the parts of the transpose of λ. We give a short and self-contained proof of this fact.