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图与组合系列讲座之三十九(Paul Terwilliger)

  发布日期:2018-11-16  浏览量:331



报告题目(一)Catalan words and q-shuffle algebras

报告题目(二)The Lusztig automorphism of the q-Onsager algebra

报 告 人: Paul Terwilliger(威斯康星大学, 教授)

报告时间: 20181119(周一)下午1700-1800

20181120(周二)下午1700-1800

报告地点:磬苑校区澳门赌搏网站大全H113

报告摘要(一)The topic of Catalan sequences appears in many textbooks on combinatorics. In fact the recent books by R. Stanley and Steven Roman are devoted to this subject and its myriad connections to other branches of mathematics. In this talk we will encounter Catalan sequences in the theory of quantum groups and q-shuffle algebras. The quantum group of interest is the quantum affine sl2 algebra, denoted Uq. Our q-shuffle algebra is obtained from the free algebra on two generators x,y by replacing the free product with a q-shuffle product due to M. Rosso. We will use Catalan sequences in x, y to obtain a PBW basis for the positive part of Uq.

This talk is nontechnical and meant for a general mathematical audience.

报告摘要(二)The q-Onsager alebra Oq is defined by two generators and two relations, called the q-Dolan/Grady relations. The algebra Oq originated in algebraic graph theory, and has been used in special functions and statistical mechanics. A finite-dimensional irreducible Oq-module is essentially the same thing as a tridiagonal pair of q-Racah type.

Recently Baseilhac and Kolb introduced an automorphism L of Oq,called the Lusztig automorphism. I will describe what happens when a finite-dimensional irreducible Oq-module is twisted via L, and discuss the significance for tridiagonal pairs.

The talk is nontechnical and meant for a general mathematical audience. Many diagrams will be drawn.

专家概况: Paul Terwilliger, an eminent mathematician, was born in 1955 in Michigan, USA. He has been a professor of University of Wisconsin at Madison since 1994. In the research area of algebraic combinatorics, he has published more than 100 papers with total citations more than 2200. He is the founder of the theory of Terwilliger algebras, which was started in his monumental papers The subconstituent algebra of an association scheme I, II, III. Since then, he is pushing back the frontiers, developing deep new ideas and finding many applications not only in combinatorics, but also in other areas of mathematics such as statistical mechanics.

欢迎各位老师、同学届时前往!


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