Linear Representations: Basics and Examples

This lecture introduces linear representations, emphasizing the importance of regular homomorphisms from a linear algebraic group to GLV. It covers the notion of isomorphism between representations, the relationship between linear actions and representations, and the concept of G modules. The instructor explains how to classify representations of C star, showing that they are always diagonalizable. The lecture also delves into the weight space decomposition, illustrating how representations can be decomposed into weight spaces. Furthermore, it explores the classification of representations of C plus, demonstrating that they correspond to nilpotent matrices in GLN. The content concludes with a comprehensive classification of all representations of C plus.