On the minimal parabolic induction

TL;DR

This paper introduces the minimal parabolic induction functor for Kac-Moody algebras, inspired by Beilinson-Bernstein's work, and explores its properties and applications in representation theory.

Contribution

It defines a new induction functor for Kac-Moody algebras and investigates its fundamental properties and implications for module extensions and annihilators.

Findings

Computed extension groups between simple highest weight modules.

Analyzed annihilators of certain simple modules.

Established basic properties of the minimal parabolic induction functor.

Abstract

Motivated by Beilinson-Bernstein's proof of the Jantzen conjectures, 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.