On the structure of simple bounded weight modules of sl(infinity), o(infinity), sp(infinity)

摘要

We study the structure of bounded simple weight sl(infinity)-, o(infinity)-, sp(infinity)-modules, which have been recently classified by D. Grantcharov and I. Penkov. Given a splitting parabolic subalgebraofwe introduce the concepts of sl(infinity), o(infinity), sp(infinity) we introduce the concepts of p-aligned and pseudo-aligned sl(infinity)-, o(infinity)-, sp(infinity)-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.