We introduce the notion of affinizations and R-matrices for arbitrary quiver Hecke algebras. It is shown that they enjoy similar properties to those for symmetric quiver Hecke algebras. We next define a duality datum and construct a tensor functor between graded module categories of quiver Hecke algebras and arising from . The functor sends finite-dimensional modules to finite-dimensional modules, and is exact when is of finite type. It is proved that affinizations of real simple modules and their R-matrices give a duality datum. Moreover, the corresponding duality functor sends a simple module to a simple module or zero when is of finite type. We give several examples of the functors from the graded module category of the quiver Hecke algebra of type , , , to that of type , , , , respectively.
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Masaki Kashiwara, Euiyong Park, Affinizations and R-matrices for quiver Hecke algebras. J. Eur. Math. Soc. 20 (2018), no. 5, pp. 1161–1193DOI 10.4171/JEMS/785