On the minimal parabolic induction

Abstract

Motivated by Beilinson–Bernstein's proof of the Jantzen conjectures [4], we define the minimal parabolic induction functor for Kac–Moody algebras, and establish some basic properties.

As applications of the formal theory, we examine first extension groups between simple highest weight modules in the category of weight modules, and analyze the annihilators of some simple highest weight modules.