On the Chow groups of hypersurfaces in symplectic Grassmannians

Let $Y$ be a Pl"ucker hypersurface in a symplectic Grassmannian $I_1 Gr(3,n)$orabisymplecticGrassmannian$I_2 Gr(3,n)$. We show that many Chow groups of $Y$ inject into cohomology.