Infinite-dimensional groups over finite fields and a related positivity problem in symmetric function theory
ABSTRACT
Sergei Kerov and Anatoly Vershik discovered a remarkable family of infinite-dimensional matrix groups over finite fields. These groups are locally compact, totally disconnected and bear some resemblance with reductive p-adic groups. The study of these infinite-dimensional groups and their representations is in the beginning stages. However, there are a number of promising results and a lot of intriguing open problems, some of which admit a reformulation in the language of symmetric functions. I will present an introduction to this area. The talk is based on joint work with Cesar Cuenca.
