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

  • Part of
  • Tomoyuki Arakawa, Peter Fiebig
  • Journal:
    Compositio Mathematica / Volume 148 / Issue 6 / November 2012
    Published online by Cambridge University Press:
    11 October 2012, pp. 1787-1810
    Print publication:
    November 2012
    • Article
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  • 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 Bernstein–Gelfand–Gelfand-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.