A Short Proof of Gamas's Theorem

Details A Short Proof of Gamas's Theorem A Short Proof of Gamas's Theorem

2009-06-25

arxiv.org/abs/0906.4769v1

Linear Algebra and its Applications Volume 430, Issues 2-3, 15 January 2009, Pages 791-794

Mathematics

Combinatorics

Scientific paper

10.1016/j.laa.2008.09.027

If \chi^\lambda is the irreducible character of the symmetric group S_n corresponding to the partition \lambda of n then we may symmetrize a tensor v_1 \otimes ... \otimes v_n by \chi^\lambda. 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 \lambda. We give a short and self-contained proof of this fact.

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