Quantum affine algebras and KLR algebras

报告题目Quantum affine algebras and KLR algebras

报告专家李建荣 (维也纳大学)



报告摘要:Recently, Baumann-Kamnitzer-Knutson introduced a remarkable algebra morphism: \bar{D} from C[N] to the field of rational functions C(a_1, ..., a_n), where N is the unipotent radical of a simply laced complex algebraic group and a_i are simple roots, in their proof of a conjecture of Muthiah about MV basis of C[N]. The algebra C[N] and a larger algebra K_0(C^{\xi}) have monoidal categorifications using representations of quantum affine algebras introduced by Hernandez and Leclerc. We defined an algebra morphism \tilde{D} from K_0(C^{\xi}) to C(a_1, ..., a_n) and proved that when restricts to C[N], \tilde{D} coincides with \bar{D}. Moreover, using \tilde{D} and \bar{D}, we can recover information of q-characters of representations of quantum affine algebras from ungraded characters of modules of KLR algebras and vice versa. This is joint work with Elie Casbi.


报告人简介:李建荣,维也纳大学研究员,主要从事表示论,特别是丛代数、量子群、组合数学以及在数学物理中的应用等方面的研究工作,相关研究工作发表于 Int. Math. Res. Not, Selecta Math., Math. Zeit. 等国际一流数学杂志。