题目：Shuffles and their braided version : from Multiple Zeta Values to quantum groups

报告人：Marc ROSSO, 巴黎西岱大学

时间：10月22日，16：00-17：00

地点：东区第五教学楼5106

摘要：Shuffles are special elements of the symmetric group, with which the algebra structure of a fundamental Hopf algebra enjoying a universal property is described.

Shuffle products appear in many domains of mathematics (combinatorics, homological algebra, interated integrals, ….), in particular in the theory of Multiple Zeta Values (MZV), which are multi variables generalizations of the classical zêta Riemann function at integer values. These MZV satisfy linear relations which are consequences of two ways to compute their products, involving respectively shuffle and quasi-shuffles of their arguments; these are at the heart in some conjectures on the algebra generated by MZV.

Shuffles can be lifted to the braid group. This gives a way to quantize the previous Hopf algebra and leads to a construction of quantum groups and some of their representations.