题目：Canonical Bases of Quantum Groups

报告人：庄司俊明 教授（同济大学）

地点：致远楼108室

时间：2025年5月23日~5月25日 13:30—15:30

Abstract: Quantum groups were introduced by Drinfeld and Jimbo, independently, around 1985. The original motivation was related to mathematical physics, but it became apparent that quantum groups provide a very useful tool for various areas of pure mathematics, such as representation theory, combinatorics, and knot theory, etc.

Canonical bases of quantum groups were introduced by Lusztig around 1990. At the same time, Kashiwara constructed crystal bases, by a completely different method, and later it was shown that those two bases are equal.

Canonical bases (or crystal bases) are important for the representation theory, but the direct computation is very hard. By the way, there exists another type of bases, called PBW bases, whose construction is more elementary. So it is useful to know the transition matrix P between canonical bases and PBW bases. In this course, we show that there exists a simple algorithm of computing P.

报告人简介：庄司俊明，现任同济大学数学科学学院教授，主要研究领域是代数群与量子群的表示论，曾获得日本代数学奖。1947年出生在日本静冈县，1970-1981年间，在东京大学分别取得了理学学士、硕士和博士学位，1975-2003年在东京理科大学分别担任过Research Assistant, Assistant Professor, Associate Professor, Professor职务，2003-2013年在名古屋大学担任Professor职务。1981年10月访问Utrecht University，1981年11月-1982年1月访问德国Bonn的Sonder Forschungs Bereich，1982年2月-9月访问美国University of Oregon。2013年入选外国专家千人计划，开启在同济的育人事业。

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