Orthogonal bundles and skew-Hamiltonian matrices

Using properties of skew-Hamiltonian matrices and classic connectedness results, we prove that the moduli space M-ort(0) (r, n) of stable rank r orthogonal vector bundles on P-2, with Chem classes (c(1), c(2)) = (0, n) and trivial splitting on the general line, is smooth irreducible of dimension (r - 2)n - ((r)(2)) for r = n and n >= 4, and r = n - 1 and n >= 8. We speculate that the result holds in greater generality.