Induced operators on symmetry classes of tensors
Chi-Kwong Li, Alexandru Zaharia · Transactions of the American Mathematical Society · 2001
Let V V be an n n -dimensional Hilbert space. Suppose H H is a subgroup of the symmetric group of degree m m , and χ : H → C \chi : H \rightarrow \mathbb C is a character of degree 1 on H H . Consider the symmetrizer on the tensor space ⨂ m V \bigotimes ^m V S ( v 1 ⊗ ⋯ ⊗ v m ) = 1 | H | ∑ σ ∈ H χ ( σ ) v σ − 1 ( 1 ) ⊗ ⋯ ⊗ v σ