arXiv subjects
Publications and source records attributed to Dimitra-Dionysia Stergiopoulou.
We determine the integral extension groups $Ext^1(Δ(h),Δ(h(k)))$ and $Ext^k(Δ(h),Δ(h(k)))$, where $Δ(h),Δ(h(k))$ are the Weyl modules of the general linear group $GL_n$ corresponding to the hook partitions $h=(a,1^b)$, $h(k)=(a+k,1^{b-k})$.
Let $K$ be an infinite field of characteristic $p>0$ and let $λ, μ$ be partitions, where $μ$ has two parts. We find sufficient arithmetic conditions on $p, λ, μ$ for the existence of a nonzero homomorphism $Δ(λ) \to Δ(μ)$ of Weyl modules for the general linear group $GL_n(K)$. Also for each $p$ we find sufficient conditions so that the corresponding homomorphism spaces have dimension at least 2.
Let $k$ be an infinite field of positive characteristic. We determine all homomorphisms between Weyl modules for $GLn(k)$, where one of the partitions is a hook. As a consequence we obtain a nonvanishing result concerning homomorphisms between Weyl modules for algebraic groups of type B, C and D when one of the partitions is a hook.
This paper concerns representations of the integral general linear group. The extension groups $Ext^2$ between any pair of hook Weyl modules are determined via a detailed study of cyclic generators and relations associated to certain extensions. As a corollary, the modular extension groups $Ext^1$ between such modules are determined.