The linkage principle for restricted critical level representations of affine KacMoody algebras

Abstract

We study the restricted category ?' for an affine KacMoody 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 Bernstein"Gelfand" Gelfand-reciprocity principle and we determine the block decomposition of the restricted category ?'. For the proofs, we need a deformed version of the classical structures, so we mostly work in a relative setting. © 2012 Foundation Compositio Mathematica.