時間：2023年1月7日，09:00
地點：騰訊會議（會議號：938 847 719）
報告人👩🦯➡️💔：張瑞斌教授（澳大利亞悉尼大學）
報告摘要：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.
報告人簡介：張瑞斌，澳大利亞悉尼大學數學與統計EON4教授, 澳大利亞數學會副主席，曾獲得澳大利亞研究委員會伊麗莎白二世獎學金(ARC Queen Elizabeth II Fellow)、澳大利亞研究委員會教授獎(ARC Australian Professorial Fellow)等諸多榮譽。張瑞斌教授主要從事李理論及其在量子物理中的應用方面的研究，在量子（超）群🤷🏼♂️、李超代數📎、低維拓撲😲👨🏽🎤、非交換幾何🛬、量子物理等方面取得了一系列有重要國際影響的研究成果，他在包括國際數學頂尖期刊Annals of Mathematics🎇🦓、J. Eur. Math. Soc.、Adv. Math、Comm. Math. Phys.🐻❄️、Proc. Lond. Math. Soc.在內的多種重要數學刊物上發表了140多篇高水平論文，被國際同行大量引用。