Let V be an n-dimensional Hilbert space. Suppose H is a subgroup of the symmetric group of degree m, and χ : H → C is a character of degree 1 on H. Consider the symmetrizer on the tensor space ⊗m V S(v1 ⊗ · · · ⊗ vm) = 1 |H| ∑ σ∈H χ(σ)vσ−1(1) ⊗ · · · ⊗ vσ−1(m) defined by H and χ. The vector space V χ (H) = S( m ⊗ V ) is a subspace of ⊗m V , called the symmetry class of tensors over V associated with H and χ. The elements in Vm χ (H) of the form S(v1⊗· · ·⊗vm) are called decomposable tensors and… CONTINUE READING