On weight modules of algebras of twisted differential operators on the projective space

TL;DR

This paper classifies and analyzes categories of weight modules over twisted differential operator algebras on projective space, identifying conditions for tameness, Koszulity, and establishing equivalences with sl(n+1)-modules.

Contribution

It provides a complete classification of blocks of weight modules, determines when they are tame or Koszul, and relates them to well-studied sl(n+1)-modules.

Findings

Identified conditions for blocks to be tame.

Proved some blocks are Koszul.

Established equivalences with sl(n+1)-modules.

Abstract

We classify blocks of categories of weight and generalized weight modules of algebras of twisted differential operators on P^n. Necessary and sufficient conditions for these blocks to be tame and proofs that some of the blocks are Koszul are provided. We also establish equivalences of categories between these blocks and categories of bounded and generalized bounded weight sl(n+1)-modules in the cases of nonintegral and singular central character.