  Given a smooth genus two curve $C$, the moduli space SU$_C(3)$ of rank three
semi-stable vector bundles on $C$ with trivial determinant is a double cover in
$\mathbb{P}^8$ branched over a sextic hypersurface, whose projective dual is
the famous Coble cubic, the unique cubic hypersurface that is singular along
the Jacobian of $C$. In this paper we continue our exploration of the
connections of such moduli spaces with the representation theory of $GL_9$,
initiated in \cite{GSW} and pursued in \cite{GS, sam-rains1, sam-rains2, bmt}.
Starting from a general trivector $v$ in $\wedge^3\mathbb{C}^9$, we construct a
Fano manifold $D_{Z_{10}}(v)$ in $G(3,9)$ as a so-called orbital degeneracy
locus, and we prove that it defines a family of Hecke lines in SU$_C(3)$. We
deduce that $D_{Z_{10}}(v)$ is isomorphic to the odd moduli space SU$_C(3,
\mathcal{O}_C(c))$ of rank three stable vector bundles on $C$ with fixed
effective determinant of degree one. We deduce that the intersection of
$D_{Z_{10}}(v)$ with a general translate of $G(3,7)$ in $G(3,9)$ is a K3
surface of genus $19$.
