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

2008/02/29 by Boris Feigin, Edward Frenkel, Leonid Rybnikov
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Affine transformation #Algebra over a field #Algebraic structures and combinatorial models #Endomorphism #Lie algebra #Mathematics #Monodromy #Pure mathematics #Verma module #Weyl algebra #math.QA #math.RT

paper · pdf · doi:10.1007/s11005-009-0308-5

9 pages

arxiv created 2009/01/30 · openalex publication_date 2009/02/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

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.

Citations

• Weyl modules and opers without monodromy
• Lectures on Wakimoto modules, opers and the center at the critical level
• Lie Group Representations on Polynomial Rings