Decomposable λ-critical tensors 1

Let λ=(λ1,…,λs) be a partition of m and let V be a finite dimensional vector space over C. We also denote by λ the irreducible character of Sm associated with the partition λ and by Vλ we denote the symmetry class of tensors associated with λ and V. Let j∈{1,…,λ1} and z∈Vλ. The concept of j-reach of z is defined. Using this concept we introduce the concept of λ-critical element of Vλ. Generalized Plücker polynomials are constructed in a way that the set of their common roots contains the set of the families of components of decomposable λ-critical elements of Vλ. The concepts and results are generalizations of those defined and proved in [4].