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

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

2009-09-23

arxiv.org/abs/0909.4214v3

Mathematics

Representation Theory

25 pages, substantially revised version, closing a gap in the earlier versions

Scientific paper

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.

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