The linkage principle for restricted critical level representations of affine Kac-Moody algebras

We study the restricted category O for an affine Kac--Moody algebra at the critical level. In particular, we prove the first part of the Feigin-Frenkel conjecture: the linkage principle for restricted Verma modules. Moreover, we prove a version of the BGGH-reciprocity principle and we determine the block decomposition of the restricted category O. For the proofs we need a deformed version of the classical structures, so we mostly work in a relative setting.