Symmetric quiver Hecke algebras and R-matrices of quantum affine algebras IV

Seok Jin Kang, Masaki Kashiwara, Myungho Kim, Se Jin Oh

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

Let Uq′(g) be a twisted affine quantum group of type AN(2) or DN(2) and let g0 be the finite-dimensional simple Lie algebra of type AN or DN. For a Dynkin quiver of type g0, we define a full subcategory CQ(2) of the category of finite-dimensional integrable Uq′(g)-modules, a twisted version of the category CQ(1) introduced by Hernandez and Leclerc. Applying the general scheme of affine Schur–Weyl duality, we construct an exact faithful KLR-type duality functor FQ(2):Rep(R)→CQ(2), where Rep (R) is the category of finite-dimensional modules over the quiver Hecke algebra R of type g0 with nilpotent actions of the generators xk. We show that FQ(2) sends any simple object to a simple object and induces a ring isomorphism [InlineEquation not available: see fulltext.].

Original languageEnglish
Pages (from-to)1987-2015
Number of pages29
JournalSelecta Mathematica, New Series
Volume22
Issue number4
DOIs
StatePublished - 1 Oct 2016

Keywords

  • Quantum affine algebra
  • Quantum group
  • Quiver Hecke algebra

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