Applications of the category of linear complexes of tilting modules associated with the category O

TL;DR

This paper employs the algebraic framework of linear complexes of tilting modules in category O to reprove known results and derive new insights about the structure of parabolic category O, bypassing geometric methods.

Contribution

It introduces an algebraic approach using linear complexes of tilting modules to analyze category O, providing new results and alternative proofs of existing theorems.

Findings

Reproves known results about category O algebraically

Derives new results on parabolic category O

Shows the effectiveness of tilting modules in category O analysis

Abstract

We use the category of linear complexes of tilting modules for the BGG category O, associated with a semi-simple complex finite-dimensional Lie algebra g, to reprove in purely algebraic way several known results about O obtained earlier by different authors using geometric methods. We also obtain several new results about the parabolic category O.