Centers for the restricted category O at the critical level over affine Kac-Moody algebras

TL;DR

This paper investigates the structure of the center of a deformed restricted category O at the critical level over affine Kac-Moody algebras, providing new insights into its algebraic properties.

Contribution

It computes the center of the deformed restricted category O at the critical level, advancing understanding of its algebraic structure and deformation theory.

Findings

Calculated the center of the deformed restricted category O

Provided explicit descriptions of algebraic structures involved

Enhanced understanding of affine Kac-Moody algebra representations

Abstract

The restricted category O at the critical level over an affine Kac-Moody algebra is a certain subcategory of the ordinary BGG-category O. We study a deformed version introduced by Arakawa and Fiebig and calculate the center of the deformed restricted category O.