On some extensions of p-restricted completely splittable GL(n)-modules

Abstract

In this paper, we calculate the space $Ext^1_{GL(n)}(L_n(λ),L_n(μ))$, where GL(n) is the general linear group of degree $n$ over an algebraically closed field of positive characteristic, $L_n(λ)$ and $L_n(μ)$ are rational irreducible GL(n)-modules with highest weights $λ$ and $μ$ respectively, the restriction of $L_n(λ)$ to any Levi subgroup of GL(n) is semisimple, $λ$ is a $p$-restricted weight and $μ$ does not strictly dominate $λ$.