Weyl Characters and Borcherds Products

This lecture covers the concepts of Weyl characters, Macdonald's identities, Borcherds products, and the properties of root systems in Euclidean space. It explores the relationships between vectors, spans, and the Weyl group, as well as the generation of Borcherds products. The lecture delves into the finite sets of non-zero vectors, the conditions for certain products, and the subgroup structures of O(E).