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Duality via convolution of W-algebras

  • Thomas Creutzig [3] ; Andrew R. Linshaw [1] ; Shigenori Nakatsuka [4] ; Ryo Sato [2]
    1. [1] University of Denver

      University of Denver

      Estados Unidos

    2. [2] Aichi Institute of Technology

      Aichi Institute of Technology

      Japón

    3. [3] Department Mathematik, FAU Erlange ,Germany n-Nürnberg,
    4. [4] Department Mathematik, FAU Erlange ,Germany
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  • Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 31, Nº. 3, 2025
  • Idioma: inglés
  • DOI: 10.1007/s00029-025-01050-9
  • Enlaces
  • Resumen

    • Feigin-Frenkel duality is the isomorphism between the principal W-algebras of a simple Lie algebra g and its Langlands dual Lie algebra L g. A generalization of this duality to a larger family of W-algebras called hook-type was recently conjectured by Gaiotto and Rapˇcák and proved by the first two authors. It says that the affine cosets of two different hook-type W-(super)algebras are isomorphic. A natural question is whether the duality between the affine cosets can be enhanced to reconstruct one W-algebra from the other. There is a convolution operation that maps a hook-type Walgebra W to a certain relative semi-infinite cohomology of W tensored with a suitable kernel VOA. The first two authors conjectured previously that this cohomology is isomorphic to the Feigin-Frenkel dual hook-type W-algebra. Our main result is a proof of this conjecture.

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