The linkage principle for restricted critical level representations of affine Kac-Moody algebras. (English) Zbl 1343.17016
Summary: We study the restricted category \(\mathcal O\) 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 Bernstein-Gelfand-Gelfand-reciprocity principle and we determine the block decomposition of the restricted category \(\mathcal O\). For the proofs, we need a deformed version of the classical structures, so we mostly work in a relative setting.
MSC:
| 17B67 | Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras |
| 17B10 | Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) |
Keywords:
linkage principleReferences:
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