Representation theory of Lie groups

Representation theory of Lie groups is a branch of mathematics that studies how Lie groups can be represented as groups of transformations on vector spaces. More formally, a representation of a Lie group \( G \) is a homomorphism from \( G \) to the general linear group GL(V) of invertible linear transformations on a vector space \( V \). This allows one to study properties of the group \( G \) through linear algebra and the geometry of vector spaces.