Weyl Modules and Opers without Monodromy

  • Edward Frenkel
  • Dennis Gaitsgory
Part of the Progress in Mathematics book series (PM, volume 279)


We prove 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. This result may be used to test the local geometric Langlands correspondence proposed in our earlier work.


Verma Module Moody Algebra Weyl Module Dominant Integral Weight Miura Transformation 
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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA
  2. 2.Department of MathematicsHarvard UniversityCambridgeUSA

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