报告时间：2024年07月02日（星期二）15:30-16:30

报告地点：翡翠湖校区科教楼B座1710室

报 告 人：Ruibin Zhang 教授

工作单位：University of Sydney

举办单位：数学学院

报告简介：

Branching rules and tensor product decompositions are two aspects of the representation theory of Lie superalgebras most frequently used in physics (particularly in building supersymmetric models of elementary particle). There is a general principle relating them to each other in the context of Howe duality. We explore this principle to develop an algebraic approach to the branching of representations of the general linear Lie superalgebra.  We construct certain super commutative algebras, called branching algebras, whose structure encodes the branching rules. This enables us to derive the branching rules for restricting any irreducible polynomial representation of the general linear Lie superalgebra to regular subalgebras. This also yields explicit formulae for the multiplicities of the irreducible sub-representations in terms of Kostka numbers.  The approach generalises to the oscillator representations of the general linear and orthosymplectic Lie superalgebras. This talk is based on the paper Soo Teck Lee, R. B. Zhang, Branching algebras for the general linear Lie superalgebra, arXiv e-prints, arXiv: 2403.11393。

报告人简介：

Ruibin Zhang，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，澳大利亚研究委员会教授奖等诸多荣誉。研究主要集中在李理论及其在量子物理中的应用，涉及量子（超）群、李超代数、低维拓扑、非交换几何等领域。特别地，在量子代数的结构和表示理论等方面取得了一系列有重要国际影响的研究成果，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等重要国际数学刊物上发表140多篇高水平论文，并被国际同行大量引用。