"Total positivity in loop groups"

Pavlo Pylyavskyy
University of Michigan

Monday, June 22, 2009
10:00 am, 845 Patterson Office Tower

Abstract:

In this work joint with Thomas Lam we define and study the totally positive part of polynomial and formal loop groups. Our motivation comes from two sources. On the one hand, we generalize Lusztig's theory of total positivity in reductive groups. On the other, we generalize the work of Aissen, Schoenberg and Whitney on totally positive sequence and aim to generalize the Edrei-Thoma theorem which is related to asymptotic representation theory of symmetric groups.