On BGG resolutions of unitary modules for quiver Hecke and Cherednik algebras

• C. Bowman ^[1] ; E. Norton ^[2] ; J. Simental ^[3]
  1. [1] University of York

     University of York

     Reino Unido

     
  2. [2] University of Kent

     University of Kent

     City of Canterbury, Reino Unido

     
  3. [3] Max Planck Institute for Mathematics

     Max Planck Institute for Mathematics

     Kreisfreie Stadt Bonn, Alemania

     

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 28, Nº. 2, 2022
• Idioma: inglés
• DOI: 10.1007/s00029-021-00739-x
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• Resumen

  • We provide a homological construction of unitary simple modules of Cherednik and Hecke algebras of type A via BGG resolutions, solving a conjecture of Berkesch–Griffeth–Sam. We vastly generalize the conjecture and its solution to cyclotomic Cherednik and Hecke algebras over arbitrary ground fields, and calculate the Betti numbers and Castelnuovo–Mumford regularity of certain symmetric linear subspace arrangements.