For let be the Weyl module for the special orthogonal group with respect to the k-th fundamental dominant weight λk of the root system of type Bn and put . It is well known that all of these modules are irreducible when char(𝔽) ≠ 2 while when char(𝔽) = 2 they admit many proper submodules. In this paper, assuming that char(𝔽) = 2, we prove that Vk admits a chain of submodules where Mi ≅ Vi for and M0 is the trivial 1-dimensional module. We also show that for the quotient Mi / Mi-2 is isomorphic to the so-called i-th Grassmann module for G. Resting on this fact we can give a geometric description of Mi-1 / Mi-2 as a submodule of the i-th Grassmann module. When 𝔽 is perfect, G ≅ Sp(2n,𝔽) and Mi / Mi-1 is isomorphic to the Weyl module for Sp(2n,𝔽) relative to the i-th fundamental dominant weight of the root system of type Cn. All irreducible sections of the latter modules are known. Thus, when 𝔽 is perfect, all irreducible sections of Vk are known as well.
© 2014 by Walter de Gruyter Berlin/Boston