Heisenberg and Kac–Moody categorification

• Jonathan Brundan ^[3] ; Alistair Savage ^[1] ; Ben Webster ^[2]
  1. [1] University of Ottawa

     University of Ottawa

     Canadá

     
  2. [2] University of Waterloo

     University of Waterloo

     Canadá

     
  3. [3] University of Oregon, USA

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 26, Nº. 5, 2020
• Idioma: inglés
• DOI: 10.1007/s00029-020-00602-5
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• Resumen

  • We show that any Abelian module category over the (degenerate or quantum) Heisenberg category satisfying suitable finiteness conditions may be viewed as a 2-representation over a corresponding Kac–Moody 2-category (and vice versa). This gives a way to construct Kac–Moody actions in many representation-theoretic examples which is independent of Rouquier’s original approach via “control by K_0.” As an application, we prove an isomorphism theorem for generalized cyclotomic quotients of these categories, extending the known isomorphism between cyclotomic quotients of type A affine Hecke algebras and quiver Hecke algebras.