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A short proof of Gamas’s theorem. (English) Zbl 1183.15022
Summary: If $$\chi^\lambda$$ is the irreducible character of $$\mathfrak S_n$$ corresponding to the partition $$\lambda$$ of $$n$$ then we may symmetrize a tensor $$v_1\otimes\cdots\otimes v_n$$ 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.

##### MSC:
 15A69 Multilinear algebra, tensor calculus 05E10 Combinatorial aspects of representation theory 20C30 Representations of finite symmetric groups
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##### References:
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