Categorification of highest weight modules via Khovanov-Lauda-Rouquier algebras

By Seok-Jin Kang, Masaki Kashiwara. 2011

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In this paper, we prove Khovanov-Lauda’s cyclotomic categorification conjecture for all symmetrizable Kac-Moody algebras. Let $U_{q}(\mathfrak{g})$ be the quantum group associated with a symmetrizable Cartan datum and let V(Λ) be the irreducible highest weight $U_{q}(\mathfrak{g})$-module with a dominant integral highest weight Λ. We prove that the cyclotomic Khovanov-Lauda-Rouquier algebra RΛ gives a categorification of V(Λ).

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/0fc60ed32096d701dc7c08c958b9dc477ea6d5cd

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Citations in the corpus

Symmetric quiver Hecke algebras and R-matrices of quantum affine algebras IV (2013, background): “Moreover, its cyclotomic quotients R , depending on dominant integral weights Λ, also provide a categorification of the integrable highest weight modules Vq(Λ) over Uq(g) [15].”
Crystals from categorified quantum groups (2009, methodology): “One should be able to deduce a classification of graded simple modules for the algebras RΛ(ν) in the symmetric case using results of [KL09] and [VV09] together with Kashiwara and Saito’s geometric construction of crystals [KS97], but the details of this argument have not appeared.”