On the structure of simple bounded weight modules of

Abstract

We study the structure of bounded simple weight -, -, -modules, which have been recently classified by D. Grantcharov and I. Penkov. Given a splitting parabolic subalgebra of we introduce the concepts of -aligned and pseudo -aligned -,-, -modules, and give necessary and sufficient conditions for bounded simple weight modules to be -aligned or pseudo -aligned. The existence of pseudo -aligned modules is a consequence of the fact that the Lie algebras considered have infinite rank.