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TITLE Affinizations and R-matrices for quiver Hecke algebras
KIAS AUTHORS Kashiwara, Masaki
JOURNAL JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2018
ARCHIVE  
ABSTRACT 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 D and construct a tensor functor F-D : Mod(gr)(R-D) -> Mod(gr)(R) between graded module categories of quiver Hecke algebras R and R-D arising from D. The functor F-D sends finite-dimensional modules to finite-dimensional modules, and is exact when R-D 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 every simple module to a simple module or zero when R-D is of finite type. We give several examples of the functors F-D from the graded module category of the quiver Hecke algebra of type D-l, C-l, Bl-1, A(l-1) to that of type A(l), A(l), B-l, B-l, respectively.
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