Restriction of irreducible modules for Spin2n + 1(K) to Spin2n(K)

Let K be an algebraically closed field of characteristic p⩾0 and let Y=Spin2n+1(K) (n⩾3) be a simply connected simple algebraic group of type Bn over K. Also let X be the subgroup of type Dn, 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].