geometric quantization and representation theory 3

Abstract: Representation theory studies groups using linear algebra: a representation turns group elements into linear transformations. Quantization turns physics into linear algebra: quantum observables are linear operators. In this short course, we describe how these topics intersect in the representation theory of simple Lie groups. In the first half, we introduce representation theory through examples, and show every finite-dimensional representation decomposes into eigenspaces called "weight spaces". In the second half, we introduce geometric quantization as a tool to construct representations starting from a chosen "highest weight".