### Abstract

Abstract. For k=1,2,...,n-1${k = 1, 2,\ldots ,n-1}$ let Vk=V(λk)${V_k = V(\lambda _k)}$ be the Weyl module for the special orthogonal group G= SO (2n+1,𝔽)${G = \mathrm {SO}(2n+1,\mathbb {F})}$ with respect to the k -th fundamental dominant weight λ k of the root system of type B n and put Vn=V(2λn)${V_n = V(2\lambda _n)}$. 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 V k admits a chain of submodules Vk=Mk⊃Mk-1⊃⋯⊃M1⊃M0⊃M-1=0${V_k = M_k \supset M_{k-1}\supset \dots \supset M_1\supset M_0 \supset M_{-1} = 0}$ where M i ≅ V i for 1,...,k-1${1,\ldots , k-1}$ and M 0 is the trivial 1-dimensional module. We also show that for i=1,2,...,k${i = 1, 2,\ldots , k}$ the quotient M i / M i -2 is isomorphic to the so-called i -th Grassmann module for G . Resting on this fact we can give a geometric description of M i -1 / M i -2 as a submodule of the i -th Grassmann module. When 𝔽 is perfect, G ≅ Sp(2 n ,𝔽) and M i / M i -1 is isomorphic to the Weyl module for Sp(2 n ,𝔽) relative to the i -th fundamental dominant weight of the root system of type C n . All irreducible sections of the latter modules are known. Thus, when 𝔽 is perfect, all irreducible sections of V k are known as well.