Structure of certain Weyl modules for the Spin groups

Let K be an algebraically closed field of characteristic p⩾0 and let W be a finite-dimensional K-vector space of dimension greater than or equal to 5. In this paper, we give the structure of certain Weyl modules for G=Spin(W) in the case where p≠2, as well as the dimension of the corresponding irreducible, finite-dimensional, rational KG-modules. In addition, we determine the composition factors of the restriction of certain irreducible, finite-dimensional, rational KSL(W)-modules to SO(W).