题 目：Quantum affine algebras and their applications to scattering amplitudes
报告人：李建荣(维也纳大学)
时 间：2024年2月3 日上午8：30—11：30
地 点：学院楼413
摘 要：Quantum affine algebra Uq(\hat{g}) is a Hopf algebra that is a $q$-deformation of the universal enveloping algebra of an affine Lie algebra \hat{g}. Hernandez and Leclerc in 2010 introduced a certain subcategory C_{\ell} of the category of finite dimensional Uq(\hat{g})-modules. They proved that K_0(C_{\ell}) has a cluster algebra structure and in the case of g=sl_k, K_0(C_{\ell}) is isomorphic to a quotient of Grassmannian cluster algebra. In joint work with Wen Chang, Bing Duan, and Chris Fraser, we proved that the dual canonical basis of a Grassmannian cluster algebra is parametrized by semistandard Young tableaux. Using results in representations of p-adic groups and quantum affine algebras, we gave a formula to compute elements in the dual canonical basis of a Grassmannian cluster algebra. In this talk, I will talk about joint work with Nick Early about a construction of prime modules of quantum affine algebras using Newton polytopes. We apply the results of prime modules to construct u-variables for Grassmannian cluster algebras which are useful in scattering amplitudes. I will also talk about joint work with James Drummond and Ömer Gürdoğan about tropicalization of quasi-automorphisms of cluster algebras. Using tropicalization, we study fixed points and orbits of Chris Fraser's braid group actions on Grassmannian cluster algebras.
报告人简介：李建荣，2012年博士毕业于兰州大学数学与统计学院并留校工作，现为维也纳大学博士后研究员，从事量子群，表示论，丛代数，数学物理等研究。现主持完成国家自然基金青年项目1项，主持完成奥地利自然科学基金1项，主持在研奥地利自然科学基金1项。在SelectaMathematica,Mathematische Zeitschrift,Int.Math.Res.Notices,J.Algebra,Algeb.Rep.Theory,J.AlgebraicComb.,J.Lietheory等国际SCI期刊上发表学术论文20余篇。
