On the Endomorphisms of Weyl Modules over Affine Kac–Moody Algebras at the Critical Level

  • Boris Feigin
  • Edward FrenkelEmail author
  • Leonid Rybnikov
Open Access


We present an independent short proof of the recently established result that the algebra of endomorphisms of a Weyl module of critical level is isomorphic to the algebra of functions on the space of monodromy-free opers on the disc with regular singularity and residue determined by the highest weight of the Weyl module. We derive this from our results about the shift of argument subalgebras.

Mathematics Subject Classification (2000)



affine Kac–Moody algebra at critical level Weyl module oper monodromy 



We thank D. Gaitsgory for useful comments on the draft of this paper.

Open Access

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Copyright information

© The Author(s) 2009

Authors and Affiliations

  1. 1.Landau Institute for Theoretical PhysicsMoscowRussia
  2. 2.Department of MathematicsUniversity of CaliforniaBerkeleyUSA
  3. 3.Institute for Theoretical and Experimental PhysicsMoscowRussia

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