報告題目：Invariants of the orthosymplectic Lie superalgebra and the super Pfaffian
時間：2015-12-9 13:30—16:35
地點：教學樓2B106
報告人：Ruibin Zhang （悉尼大學）
報告摘要：The invariant theory of the orthosymplectic Lie superalgebra osp(V) is more intricate than that of the orthosymplectic supergroup OSp(V). For example, the endomorphism algebra End_{OSp}(V)(V^{\otimes r}) over the orthosymplectic supergroup is a quotient of the Brauer algebra of degree r (with parameter equalto the superdimension of V) as proved recently, but the endomorphism algebra End_{osp}(V)(V^{\otimes r}) over the orthosymplectic superalgebra contains elements which are not Brauer-like. We will describe explicitly some osp(V)-invariants which are referred to as super Pfaffians, and show that the OSp(V)-invariants and super Pfaffians together generate all the osp(V)-invariants. This talk is a report on some of the results in the papers
? ? (1) G.I. Lehrer, R.B. Zhang, Invariants of the orthosymplectic Lie superalgebra and super Pfaffians. arXiv:1507.01329.
? ? (2) P. Deligne, G. I. Lehrer, R. B. Zhang, The first fundamental theorem of invariant theory for the orthosymplectic super group. arXiv:1508.04202.
報告人簡介：張瑞斌，澳大利亞悉尼大學數學與統計學院教授，曾獲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，擔任Taiwanese Journal of Mathematics編委以及眾多國際期刊評委，澳大利亞研究委員會和美國國家安全局特約研究評審顧問。受邀在眾多國家進行過學術演講和訪問。主要研究工作是李理論及其在量子物理中的應用，在國際重要學術期刊如《Annals of Mathematics數學年刊》、《Journal of Mathematical Physics數學物理雜志》、《Advances in Mathematics數學進展》、《Journal of Algebra代數雜志》、《Transactions of American Mathematical Society美國數學學會會報》發表論文120余篇，論文被他人引用1200余次，在量子超群、李超代數、低維拓撲、非交換幾何、量子物理等取得重要的科研成果,在國際數學界有重要的學術影響。?