Orthogonal invariants of skew-symmetric matrices
The algebra of invariants of d-tuples of n × 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.