Finite dimensional representations of root graded Lie algebras $\mathfrak{g}_{N,\rho} (\mathbb{C}

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Finite dimensional representations of root graded Lie algebras $\mathfrak{g}_{N,\rho} (\mathbb{C}_q)$

时间：2025年10月28日 21:14 点击数：

报告人：陈洪佳

报告地点：腾讯会议ID: 956-869-392

报告时间：2025年10月31日星期五10:00-10:45

邀请人：陈良云

报告摘要：

Extended affine Lie algebras (EALA) were first introduced by physicists Hoegh-Krohn and Torresani, as a generalization of finite-dimensional simple Lie algebras and affine Kac-Moody Lie algebras over the complex numbers $\mathbb{C}$. In 2006, Yoshii gave a simple characterization of the core of an EALA. Namely, he showed that the core of any EALA is a Lie torus, and any centreless Lie torus is the centreless core of some EALA. In this talk, the finite-dimensional irreducible representations of the nullity 2 centreless core $\mathfrak{g}_{N,\rho}(\mathbb{C}_q)$ will be discussed by investigating the structure of the root graded Lie algebras $\mathfrak{g}_{N,\rho}(R)$. This talk is based on the joint work with Sandeep Bhargava, Qi Chen and Yun Gao.

主讲人简介：

陈洪佳，中国科学技术大学数学科学学院教授、博士生导师，国家级高层次青年人才。主要从事李代数、量子群及其表示理论的研究，相关成果发表在《Adv. Math.》、《Trans. Amer. Math. Soc.》、《J. Lond. Math. Soc.》、《Math. Z.》、《Forum Math.》、《J. Algebra》、《J. Pure Appl. Algebra》等知名期刊。