Colloquium Mathematics - Ivan Penkov, University of Bremen

Title: The classical Pieri rule and tensor categories of sl(infty)-modules

Abstract:

My aim is to outline a direction of research within the representation theory of infinite-dimensional Lie algebras.Here one encounters infinite-dimensional analogues of some cornerstones of finite-dimensional representation theory. One of these cornerstones is the Pieri rule for tensoring with the natural representation of sl(n). I will start the talk byrecalling the Pieri rule, and then will try to explain how it works in some infinite-dimensional situations. Hopefully, this will give usa glimpse on the structure of some highest weight tensor categories of representations of the Lie algebra sl(infty).