Lectures related to Lie Algebra: Representations and Symmetry Groups

Explores the classification and properties of simple complex Lie algebras, emphasizing their connection with Lie groups.

Delves into Macdonald identities, covering affine root systems, modular forms, and Lie algebras.

Explores nilpotent Lie groups, their orbits, and adjoint actions, illustrating simplicity and form.

Delves into symmetries in physics, covering group theory, perturbation, and quantification.

Covers the Weil representation, Heis operators, Stone-Neumann theorem, unitary operators, Lie algebra structure, and symplectic form.

Covers examples of group algebra decomposition and simple infinite-dimensional algebras.

Explores the Kirillov paradigm for the Heisenberg group and unitary representations.

Explores the dynamical consequences of symmetry, emphasizing conservation laws and the role of Noether currents.