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

• Seok-Jin Kang ^[3] ; Masaki Kashiwara ^[1] ; Myungho Kim ^[4] ; Se-Jin Oh ^[2]
  1. [1] Kyoto University

     Kyoto University

     Kamigyō-ku, Japón

     
  2. [2] Ewha Womans University

     Ewha Womans University

     Corea del Sur

     
  3. [3] Gwanak Wiberpolis 101-1601
  4. [4] Kyunghee University

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 22, Nº. 4 (Special Issue: The Mathematics of Joseph Bernstein), 2016, págs. 1987-2015
• Idioma: inglés
• DOI: 10.1007/s00029-016-0267-5
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• Resumen

  • Let U q (g) be a twisted affine quantum group of type A(2) N or D(2) N 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 C(2) Q of the category of finite-dimensional integrable U q (g)-modules, a twisted version of the category C(1) Q introduced by Hernandez and Leclerc. Applying the general scheme of affine Schur–Weyl duality, we construct an exact faithful KLR-type duality functor F(2) Q : Rep(R) → C(2) Q , where Rep(R) is the category of finite-dimensional modules over the quiver Hecke algebra R of type