Geometric Quantization: Representation Theory

This lecture covers the concept of geometric quantization in representation theory, focusing on the group SO3(R) acting naturally on R³ and the homogenous polynomials of degrees. It discusses the rotation of degrees around the Z-axis and the conjugation of the group. The lecture also delves into the application of SO₂(R) on R² and the corresponding homogenous polynomials. Various mathematical operations and transformations are explored, such as the action of SO₂(R) on R² and R³, the dimensionality of vector spaces, and the general formulas for different mathematical expressions.