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Let $K$ be an algebraically closed field of characteristic $p\geqslant 0$ andlet $Y=\mbox{Spin}_{2n+1}(K)$ $(n\geqslant 3)$ be a simply connected simplealgebraic 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 thestabilizer of a non-singular one-dimensional subspace of the natural module for$Y.$ In this paper, we give a complete set of isomorphism classes offinite-dimensional, irreducible, rational $KY$-modules on which $X$ acts withexactly two composition factors.

Restriction of irreducible modules for $\mbox{Spin}_{2n+1}(K)$ to $\mbox{Spin}_{2n}(K)$