報(bào)告題目：Invariants of the orthosymplectic Lie superalgebra and the super Pfaffian
時(shí)間：2015-12-9 13:30—16:35
地點(diǎn)：教學(xué)樓2B106
報(bào)告人：Ruibin Zhang （悉尼大學(xué)）
報(bào)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(bào)告人簡介：張瑞斌，澳大利亞悉尼大學(xué)數(shù)學(xué)與統(tǒng)計(jì)學(xué)院教授，曾獲澳大利亞研究委員會(huì)伊麗莎白二世獎(jiǎng)學(xué)金（ARC Queen Elizabeth II Fellow）、澳大利亞研究委員會(huì)教授獎(jiǎng)（ARC Australian Professorial Fellow）等諸多榮譽(yù)，擔(dān)任Taiwanese Journal of Mathematics編委以及眾多國際期刊評(píng)委，澳大利亞研究委員會(huì)和美國國家安全局特約研究評(píng)審顧問。受邀在眾多國家進(jìn)行過學(xué)術(shù)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(yīng)用，在國際重要學(xué)術(shù)期刊如《Annals of Mathematics數(shù)學(xué)年刊》、《Journal of Mathematical Physics數(shù)學(xué)物理雜志》、《Advances in Mathematics數(shù)學(xué)進(jìn)展》、《Journal of Algebra代數(shù)雜志》、《Transactions of American Mathematical Society美國數(shù)學(xué)學(xué)會(huì)會(huì)報(bào)》發(fā)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(shù)、低維拓?fù)洹⒎墙粨Q幾何、量子物理等取得重要的科研成果,在國際數(shù)學(xué)界有重要的學(xué)術(shù)影響。?