Centers for the restricted category $$\mathcal {O}$$ O at the critical level over affine Kac–Moody algebras

Abstract

The restricted category \(\mathcal {O}\) at the critical level over an affine Kac–Moody algebra is a certain subcategory of the ordinary BGG-category \(\mathcal {O}\). We study a deformed version introduced by Arakawa and Fiebig and calculate the center of the deformed restricted category \(\mathcal {O}\). This complements a result of Fiebig which describes the center of the non-restricted category \(\mathcal {O}\) outside the critical hyperplanes over a symmetrizable Kac–Moody algebra.