数学学科2020系列学术报告十九——二十一 （量子群结构及其表示理论系列报告）

报告人：陈晓煜（博士），华东师范大学

题目: The principal series representations of reductive groups with Frobenius maps

时间：2020/11/18 10:00-10:50   腾讯会议：201946733，密码：201118

摘要：Let G be a connected reductive group defined over Fp and B be a

　　Borel subgroup of G (not necessarily defined over Fp). Let q be the cover of Fp. We show that for each (one dimensional) character  of B (not necessarily rational), the principal series representation has unique simple quotient. In particular, there is an unique (up to isomorphism) irreducible module containing the character as a kB-submodule, and moreover, the irreducible module is isomorphic to a parabolic induction from a finite dimensional irreducible |L-module for some Levi subgroup L of G. Thus, we classified and constructed all (abstract) irreducible kG-module with B-stable line. As a byproduct, we give a new proof of the result of Borel and Tits on the structure of finite dimensional irreducible kG-modules. We also give a necessary and sufficient condition for M(/theta) being finite length and determine composition factors when M(/theta) has finite length.

报告人：胡乃红（教授），华东师范大学

题目: Classification of finite-dimensional Hopf algebras over dual Radford algebras

时间：2020/11/18 14:30-15:30   腾讯会议：会议号：201946733，密码：201118

摘要： In this talk, we considered the classification of finite-dimensional Hopf algebras over dual Radford algebra.

报告人简介：

　　胡乃红，华东师大数学系教授，博士生导师，德国洪堡学者，从事李代数与量子群的结构与表示论研究，目前主要研究Hopf代数分类及其范畴化理论。已在国际学术刊物发表论文60多篇，曾获得教育部霍英东青年教师奖（研究类）二等奖，第三届教育部青年教师奖，上海市启明星计划和追踪计划，上海市优秀青年教师称号，多次主持国家自然科学基金面上项目，教育部博士点基金项目，两次参与国家自然科学基金重点项目，并与美国北卡州立大学景乃桓教授合作，获得国家自然科学基金海外优秀青年合作研究基金（即杰出青年基金B类）支持。

报告人：杨高(博士)，哈尔滨工程大学

题目: Cell theories and beyond

时间：2020/11/18 15：40--16:30，腾讯会议：会议号：201946733，密码：201118

摘要：This talk will be an elementary explanation on various cell theories, their connections and their relations with Humphreys conjecture and character formula.