Gamas's Theorem
Gamas's theorem is a result in multilinear algebra which states the necessary and sufficient conditions for a tensor symmetrized by an irreducible representation of the symmetric group  to be zero. It was proven in 1988 by Carlos Gamas. Additional proofs have been given by Pate and Berget. Statement of the theorem 

Let  be a finite-dimensional complex vector space and  be a partition of . From the representation theory of the symmetric group  it is known that the partition  corresponds to an irreducible representation of . Let  be the character of this representation. The tensor  symmetrized by  is defined to be 

where  is the identity element of . Gamas's theorem states that the above symmetrized tensor is non-zero if and only if it is possible to partition the set of vectors  into linearly independent sets whose sizes are in bijection with the lengths of the columns of the partition . See also
Algebraic combinatorics
Immanant
Schur polynomial

References

Algebraic combinatorics
Theorems
Multilinear algebra