2013/04/30 by Seok-Jin Kang, Masaki Kashiwara, Myungho Kim · 1 citation
Mathematics · #math.RT #math.QA #msc:81R50 #msc:16G #msc:16T25 #msc:17B37
paper · pdf · doi:10.1007/s00222-017-0754-0
published as Invent. math. 211, 591--685 (2018) · 80 pages. arXiv:1209.3536 is merged to this paper. Version 2: We proved that the Grothendieck group $K(T_J)$ is isomorphic to the t-deformation of $K(C_J)$. Version 3: We made corrections mainly according to Correction in Invent. Math. 216 (2019), no. 2, 597--599
arxiv created 2021/03/26 · arxiv updated 2021/03/29
Let J be a set of pairs consisting of good modules over an affine quantum algebra and invertible elements. The distribution of poles of the normalized R-matrices yields Khovanov-Lauda-Rouquier algebras RJ. We define a functor F from the category SJ of finite-dimensional graded RJ-modules to the category of finite-dimensional integrable Uq(g)-modules. The functor F sends convolution products of RJ-modules to tensor products of Uq(g)-modules. It is exact if RJ is of finite type A,D,E. When J is the vector representation of A(1)n-1, we recover the affine Schur-Weyl duality. Focusing on this case, we obtain an abelian rigid graded tensor category TJ by localizing the category SJ. The functor F factors through TJ. Moreover, the Grothendieck ring of the category CJ, the image of F, is isomorphic to the Grothendieck ring of TJ at q=1.