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:2018年11月19日(周一)下午17：00-18：00
2018年11月20日(周二)下午17：00-18：00
报告地点:磬苑校区数学科学学院H113
报告摘要（一）： The topic of Catalan sequences appears in many textbookson combinatorics. In fact the recent books by R. Stanley and StevenRoman are devoted to this subject and its myriad connectionsto other branches of mathematics. In this talk we will encounterCatalan 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 generatorsx,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 positivepart 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 tworelations, called the q-Dolan/Grady relations. The algebra Oq originatedin algebraic graph theory, and has been used in special functions andstatistical mechanics. A finite-dimensional irreducible Oq-module isessentially 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 afinite-dimensional irreducible Oq-module is twisted via L, and discussthe significance for tridiagonal pairs.
The talk is nontechnical and meant for a general mathematical audience. Many diagrams will be drawn.
欢迎各位老师、同学届时前往！
科学技术处
2018年11月16日