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
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.