Identical relations for the forms with a Young symmetry (Q1208685)

Let \({\mathcal T}\) be a fixed Young tableau and \(e_{\mathcal T}\) the corresponding Young symmetrizer. It is shown in the paper that a multilinear form has \(e_{\mathcal T}\)-symmetry if and only if it satisfies identities of two types. The first type is the skew-symmetry in variables whose indices are in the same column of \({\mathcal T}\). The second type generalizes the Jacobi identity. In addition, a generalization of Garnir identities is given.