Localizations for quiver Hecke algebras

2019/01/27 by Kashiwara, Masaki, Kim, Myungho, Oh, Se-jin +1
#16D90 #18D10 #81R10 #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1901.09319

Abstract

We provide the localization procedure for monoidal categories by a real commuting family of braiders. For an element w of the Weyl group, \mathscrC_w is a subcategory of modules over quiver Hecke algebra which categorifies the quantum unipotent coordinate algebra A_q[\mathfrakn(w)]. We construct the localization \widetilde\mathscrC_w of \mathscrC_w by adding the inverses of simple modules which correspond to the frozen variables in the quantum cluster algebra A_q[\mathfrakn(w)]. The localization \widetilde\mathscrC_w is left rigid and we expect that it is rigid.

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