The Classification of Finite-Dimensional sl_2(C)-modules

event Thursday, March 30, 2023
access_time 5:05pm (CDT)
room PHSC 1105

Abstract: We follow Mazorchuk's lectures on \(sl_2(\mathbb{C})\)-modules. We begin with an overview of the lie algebra \(sl_2(\mathbb{C}) = g\) and \(g\)-modules. We then prove the classification of simple finite-dimensional \(g\)-modules. Using this classification, we discuss finite-dimensional modules in general by showing that they are always semi-simple. Given time, we end with an outline of what tensor products of these finite-dimensional modules look like.

For more information on this event, please contact Tomoya Tatsuno.