ON SOME EXTENSIONS OF p-RESTRICTED COMPLETELY SPLITTABLE GL(n)-MODULES

摘要

In this paper, we calculate the space Ext_(GL(n))~1 (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 .