Algebra and Logic Seminar - 15/3/2016

Tuesday, 15 March 2016, 2:00 p.m.

Lecturer: Carlos André (CEAFEL & DM, Universidade de Lisboa)

Title: "Extreme supercharacters of the infinite unitriangular group"

Local: Sala de seminários, Edifício VII

Faculdade de Ciências e Tecnologia, Quinta da Torre, Caparica

Abstract: We define extreme supercharacters of the infinite unitriangular group and discuss their connections with the combinatorics of set partitions. 
We introduce the ramification scheme associated with the classical supercharacter theories of the finite unitriangular groups and describe how extreme supercharacters of the infinite unitriangular group appear as weak limits of supercharacters of those. 
In order to prove that the set of extreme supercharacters is closed (with respect to the topology of weak convergence), we will deform the ramification sheme using appropriate operations of induction and restriction and show that the resulting scheme is multiplicative and determines a convenient Riesz ring.