The Loewy series of principal indecomposable modules in the regular nilpotent representations of 𝔰𝔩(3,k)

Abstract

Let [Formula: see text] be a simple Lie algebra of type [Formula: see text] over an algebraically closed field [Formula: see text] of prime characteristic [Formula: see text] and [Formula: see text] be the reduced enveloping algebra of [Formula: see text]. In this paper, when the [Formula: see text]-character [Formula: see text] is regular nilpotent and has standard Levi form, we precisely determine the Lowey series of principal indecomposable [Formula: see text]-modules and the dimensions for the self-extension of irreducible [Formula: see text]-modules.