Pavlo Pylyavskyy

University of Michigan

Total positivity in loop groups

The talk is based on joint work with Thomas Lam. We study infinite
products of Chevalley generators in the formal loop group. I will
describe the formalism of infinite sequences of braid moves, called a
braid limit. I will relate this to a partial order, called the limit
weak order, on infinite reduced words. I will also explain the original
motivation for this work. This includes generalizing both Lusztig's
theory of total positivity in reductive groups and the Edrei-Thoma
theorem.