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吴文俊数学重点实验室代数学系列报告之一百零一【Dr. Huilan Li】
报告题目:Combinatorial Hopf Algebras and Representation Theory of Towers of Algebras

报告人:Dr. Huilan Li  山东师范大学

时间:12月12日(周一)下午4:00—5:00

地点:管研楼1518教室

摘要:We introduce by way of axioms, a general notion of a tower of algebras and study two Grothendieck groups on this tower linked by a natural paring. Using representation theory, we show that our axioms give a structure of graded Hopf algebras on each Grothendieck groups and these structures are dual to each other. Hivert and Nzeutzhap, and independently Lam and Shimozono constructed dual graded graphs from Hopf algebras. Applying the composition of the two constructions, we show that the dimension of the nth component of a tower of algebras is r^n*n!, where r is the dimension of the first component. Furthermore, we identify two seemingly disparate structures: supercharacters, a useful way of doing Fourier analysis on the group of unipotentuppertriangular matrices with coefficients in a finite field, and the ring of symmetric functions in noncommuting variables.

邀请人:陈洪佳

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中国科学院吴文俊数学重点实验室