Orthogonal invariants of skew-symmetric matrices

Abstract

The algebra of invariants of d-tuples of n x n skew-symmetric matrices under the action of the orthogonal group by simultaneous conjugation is considered over an infinite field of characteristic different from two. For n=3 and d>0 a minimal set of generators is established. A homogeneous system of parameters (i.e., an algebraically independent set such that the algebra of invariants is a finitely generated free module over subalgebra generated by this set) is described for n=3 and d>0, for n=4 and d=2,3, for n=5 and d=2.