时间：2023年1月7日，09:00
地点：腾讯会议（会议号：938 847 719）
报告人：张瑞斌教授（澳大利亚悉尼大学）
报告摘要：We construct and study a diagram category, referred to as a diagrammatic affine Brauer category, whose morphisms are linear combinations of polar enhancements of Brauer diagrams, and the endomorphism algebra of each of its objects is a quotient of an algebra of chord diagrams. It contains a subcategory isomorphic to the Brauer category; and a particular quotient of it yields an analogue of the affine Temperley-Lieb category, whose structure is understood thoroughly. We construct a functor from the diagrammatic affine Brauer category to the full subcategory of modules for the Lie superalgebra osp(V) with objects $M\otimes V^{\otimes r}$ for all r=0, 1, …, where M is an arbitrary module, and V is the natural module. When M is the universal enveloping superalgebra U(osp(V)) itself, this functor provides an effective tool to study U(osp(V)). An analysis of this functor leads to a diagrammatic construction of explicit generators for the centre of the universal enveloping superalgebra and, in the special cases when V is purely even or purely odd, a categorical interpretation of certain ``characteristic identities'' of the orthogonal and symplectic Lie algebras. These characteristic identities have been widely studied in the mathematical physics literature. This is joint work with Gus Lehrer.
报告人简介：张瑞斌，澳大利亚悉尼大学数学与统计学院教授, 澳大利亚数学会副主席，曾获得澳大利亚研究委员会伊丽莎白二世奖学金(ARC Queen Elizabeth II Fellow)、澳大利亚研究委员会教授奖(ARC Australian Professorial Fellow)等诸多荣誉。张瑞斌教授主要从事李理论及其在量子物理中的应用方面的研究，在量子（超）群、李超代数、低维拓扑、非交换几何、量子物理等方面取得了一系列有重要国际影响的研究成果，他在包括国际数学顶尖期刊Annals of Mathematics、J. Eur. Math. Soc.、Adv. Math、Comm. Math. Phys.、Proc. Lond. Math. Soc.在内的多种重要数学刊物上发表了140多篇高水平论文，被国际同行大量引用。