Rank k Vectors in Symmetry Classes of Tensors

Abstract

Let F be a field, G a subgroup of Sm, the symmetric group of degree m, and χ a linear character on G, i.e., a homomorphism of G into the multiplicative group of F. Let V1,...,Vm be vector spaces over F such that Vi = Vσ(i) for i=1,…,m and for all σ∈G. If W is a vector space over F, then a m-multilinear function is said to be symmetric with respect to G and χ iffor any σ ∊ G and for arbitrary xi ∊ Vi.