報告時間：2024年07月02日（星期二）15:30-16:30
報告地點：翡翠湖校區科教樓B座1710室
報 告 人：Ruibin Zhang 教授
工作單位：University of Sydney
舉辦單位：數學學院
報告簡介：
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。
報告人簡介：
Ruibin Zhang，澳大利亞悉尼大學數學與統計學院教授，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，澳大利亞研究委員會教授獎等諸多榮譽。研究主要集中在李理論及其在量子物理中的應用，涉及量子（超）群、李超代數、低維拓撲、非交換幾何等領域。特別地，在量子代數的結構和表示理論等方面取得了一系列有重要國際影響的研究成果，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等重要國際數學刊物上發表140多篇高水平論文，并被國際同行大量引用。
