Geodesic
Affinizations and R-matrices for quiver Hecke algebras
Journal of the European Mathematical Society, Tome 20 (2018) no. 5, pp. 1161-1193 Cet article a éte moissonné depuis la source EMS Press

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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 FD:Modg​r(RD)→Modg​r(R) between graded module categories of quiver Hecke algebras R and RD arising from D. The functor FD sends finite-dimensional modules to finite-dimensional modules, and is exact when RD 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 RD is of finite type. We give several examples of the functors FD from the graded module category of the quiver Hecke algebra of type Dl​, Cl​, Bl−1​, Al−1​ to that of type Al​, Al​, Bl​, Bl​, respectively.
DOI : 10.4171/jems/785
Classification : 16-XX, 17-XX, 81-XX
Keywords: Quiver Hecke algebra, affinization, R-matrix, duality functor 
@article{JEMS_2018_20_5_a3,
     author = {Masaki Kashiwara and Euiyong Park},
     title = {Affinizations and {R-matrices} for quiver {Hecke} algebras},
     journal = {Journal of the European Mathematical Society},
     pages = {1161--1193},
     year = {2018},
     volume = {20},
     number = {5},
     doi = {10.4171/jems/785},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/785/}
}
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Masaki Kashiwara; Euiyong Park. Affinizations and R-matrices for quiver Hecke algebras. Journal of the European Mathematical Society, Tome 20 (2018) no. 5, pp. 1161-1193. doi: 10.4171/jems/785

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