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Quantum affine algebras and Grassmannians

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讲座题目:Quantum affine algebras and Grassmannians
讲座人: 李建荣
讲座时间:9:30
讲座日期:2019-10-24
地点:长安校区 数学与信息科学学院多功能厅

讲座内容简介:

Let and the corresponding quantum affine algebra.Hernandez and Leclerc proved that there is an isomorphism from the Grothendieck ring of a certain subcategory of finite-dimensional -modules to a certain quotient of a Grassmannian cluster algebra. We proved that this isomorphism induces an isomorphism from the monoid of dominant monomials to the monoid of semi-standard Young tableaux. Using this result and the results of Qin and the results of Kashiwara, Kim, Oh, and Park, we have that every cluster monomial (resp. cluster variable) in a Grassmannian cluster algebra is of the form for some real (resp. prime real) rectangular semi-standard Young tableau T, where is certain map obtained from a formula of Arakawa-Suzuki.We also translated Arakawa--Suzuki's formula to the setting of q-characters and apply it to study real modules, prime modules, and compatibility of cluster variables. This is joint work with Wen Chang, Bing Duan, and Chris Fraser.

讲座人简介:
李建荣,奥地利格拉茨大学博士后。2012年在兰州大学获得博士学位。2013年到2016年在兰州大学数学与统计学院任讲师。曾在以色列希伯来大学,威茨曼科学研究所做博士后。在国际知名期刊 “Int. Math. Res. Not. IMRN”、“Journal of Lie Theory”、“Journal of Algebra”、“J. Algebraic Combin.”、“Algebras and Representation Theory”等上发表论文18篇。主持完成国家自然科学基金青年基金项目1项。

 

 
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