Speaker
Description
Given the scientific diversity of the audience, I will give a relatively elementary talk. My hope is that participants will be able to remember the main ideas, and that this will be in the spirit of Ivan Todorov who very much appreciated lectures with an educational emphasis.
Hermann Weyl's famous semisimplicity theorem is a basic tool when studying finite-dimensional representations of the Lie algebra $sl(n)$. However, this theorem applies to each n separately. When one puts together all $n$, and considers the direct limit Lie algebra $sl(\infty)$, the theorem no longer holds. The main purpose of the talk will be to show that the somewhat boring semisimplicity gets replaced by the appearance of an non-semisimple category having the nicest possible properties. These include finite-dimensional Homs and Exts, Koszulity, and Koszul self-duality. The talk will be concluded by taking to infinity
another icon in representation theory: the Pieri rule.