Restriction of irreducible modules for Spin2+1(K) to Spin2(K)

Let K be an algebraically closed field of characteristic $p\geq0$ and let $Y=SPin_{2n+1}(K) (n\geq3)$ be a simply connected simple algebraic group of type $B_n$ over $K$. Also let $X$ be the subgroup of type $D_n$, embedded in $Y$ in the usual way, as the derived subgroup of the stabilizer of a non-singular one-dimensional subspace of the natural module for $Y$. In this paper, we give a complete set of isomorphism classes of finite-dimensional, irreducible, rational $KY$-modules on which $X$ acts with exactly two composition factors, completing the work of Ford in [12].