Lectures related to Cartan subalgebra

Explores the proof of the Weyl character formula for finite-dimensional representations of semisimple Lie algebras.

Explores gauge symmetries in quantum field theory, emphasizing invariance under transformations and the role of ghost fields.

Explores the concept of diagonalizable groups and their properties in linear algebraic groups.

Covers the proofs related to non-diagonalizable cases and linear applications in IR³.

Explores the properties and equivalence of diagonalizable groups, including regularity and conjugacy.

Explores the scenarios of a matrix with a triple eigenvalue and its basis representation in R^3.

Explores weight space decomposition and proves that a connected linear algebraic group with all semi-simple elements must be a torus.