Subquotient categories of the affine category O at the critical level

TL;DR

This paper introduces subquotient categories within the affine category O at the critical level and demonstrates their realization through moment graph sheaves, linking representation theory and geometric methods.

Contribution

It presents a novel construction of subquotient categories at the critical level and connects them to geometric realizations via moment graph sheaves.

Findings

Subquotient categories are explicitly constructed at the critical level.

Some subquotient categories are realized through moment graph sheaves.

The work bridges representation theory and geometric methods in category O.

Abstract

We introduce subquotient categories of the restricted affine category O at the critical level and show that some of them have a realization in terms of moment graph sheaves.