On the subgeneric restricted blocks of affine category O at the critical level

TL;DR

This paper characterizes the endomorphism algebra of a projective generator within a specific subcategory of affine Kac-Moody algebra representations at the critical level, advancing understanding of category O structures.

Contribution

It explicitly determines the endomorphism algebra for a subgeneric restricted block of affine category O at the critical level, a novel result in the representation theory of affine algebras.

Findings

Explicit description of the endomorphism algebra

Identification of structure in subgeneric restricted blocks

Advancement in understanding affine category O at critical level

Abstract

We determine the endomorphism algebra of a projective generator in a subgeneric restricted block of the critical level category O over an affine Kac-Moody algebra.