R-matrices for quantum affine algebras and Khovanov-Lauda-Rouquier algebras, I

2012/09/17 by Seok‐Jin Kang, Masaki Kashiwara, Kang, Seok-Jin +3
Mathematics · Physics and Astronomy · #81R50 (Primary) 20C08 (Secondary) #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1209.3536

openalex publication_date 2012/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let us consider a finite set of pairs consisting of good U'_q(g)-modules and invertible elements. The distribution of poles of normalized R-matrices yields Khovanov-Lauda-Rouquier algebras We define a functor from the category of finite-dimensional modules over the KLR algebra to the category of finite-dimensional U_q'(g)-modules. We show that the functor sends convolution products to tensor products and is exact if the KLR albera is of type A, D, E.

Citations

• 2-Kac-Moody algebras

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