Invariants for sets of vectors and rank 2 tensors, and differential invariants for vector functions

Abstract

We outline an algorithm for construction of functional bases of absolute invariants under the rotation group for sets of rank 2 tensors and vectors in the Euclidean space of arbitrary dimension. We will use our earlier results for symmetric tensors and add results for sets including antisymmetric tensors of rank 2. That allowed, in particular, constructing of functional bases of differential invariants for vector functions, in particular, of first-order invariants of Poincar\'e algebra (invariance algebra of Maxwell equations for vector potential).