Localizations for quiver hecke algebras

Masaki Kashiwara, Myungho Kim, Se Jin Oh, Euiyong Park

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


In this paper, we provide a generalization of the localization procedure for monoidal categories developed in [12] by Kang-Kashiwara-Kim by introducing the notions of braiders and a real commuting family of braiders. Let R be a quiver Hecke algebra of arbitrary symmetrizable type and R-gmod the category of finite-dimensional graded R-modules. For an element w of the Weyl group, Cw is the subcategory of R-gmod which categorifies the quantum unipotent coordinate algebra Aq (n(w)). We construct the localization C˜w of Cw by adding the inverses of simple modules M(wΛi, Λi ) which correspond to the frozen variables in the quantum cluster algebra Aq (n(w)). The localization C˜w is left rigid and it is conjectured that C˜w is rigid.

Original languageEnglish
Pages (from-to)1465-1548
Number of pages84
JournalPure and Applied Mathematics Quarterly
Issue number4
StatePublished - 2021


  • Categorification
  • Localization
  • Monoidal category
  • Quantum unipotent coordinate ring
  • Quiver Hecke algebra


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