On the multilinearity partition of an irreducible character

Abstract

The concept of k-dimension of a family of vectors is introduced. Using this concept we are able to define the k-index of a symmetry class of tensors, generalizing the Marcus—Chollet index. Both notions enable us to associate to each irreducible character of a subgroup G of Sm a partition of m. It is also proved that if G=Sm this partition coincides with the partition usually associated with the irreducible characters of Sm .