Equality of immanantal decomposable tensors (Q1779383)

The concept of tensor product has been extended to the notion of symmetry class of tensors to deal with the symmetry in multilinear mappings. The authors present a necessary and sufficient condition for the equality of immanantal decomposable tensors with symmetry associated with irreducible characters of the form \((p,\dots,p)\). The exterior powers and the symmetric powers of V are immanantal symmetry classes associated with irreducible characters of this form. The conditions they present ``mix'' the avove conditions for the exterior powers and the symmetric powers. Section 3 is devoted to the study of decomposable tensors. This paper addresses conditions for equality of immanantal decomposable tensors. A theorem of the main result is given in Section 4.