Algebraic Geometry Working Seminar

Tuesday, July 5, 2022 1:30 pm - 1:30 pm EDT

Nicole Kitt, Department of Pure Mathematics, University of Waterloo

"Crash course on the representation theory of complex semi-simple Lie algebras - Part 1"

Given a Lie group G, its tangent space at the identity gives rise to a Lie algebra. It turns out that when G is simply connected, its representations are in one-to-one correspondence with the representations of its Lie algebra. This is very nice, since it allows us to linearize the problem of classifying representations of simply connected Lie groups by converting it to a problem about maps between vector spaces. The goal of these talks is to give a brief overview of how the classification of finite-dimensional representations of (semi-simple) Lie algebras works. We will use the special linear group SLn as our prototypical example throughout.

In the first talk, we begin by defining Lie groups, Lie algebras, and their representations. We will then quickly motivate why we care to look at such representations, and briefly see how the 1-1 correspondence above works. Then we will completely classify the representations of SL2, which is the simplest example to consider.

This seminar will be held jointly online and in person:

  • Room: MC 5403
  • Zoom information: Meeting ID: 817 1030 9714; Passcode: 063438