Lie Algebras and Representations

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Explores the transformation of vectors and tensors in quantum physics, emphasizing Lie groups and algebras.

Explores Lie groups, scalar fields, and vector spaces transformations.

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

Covers Lie algebra, group representations, symmetry groups, and Schur's lemma in the context of symmetry and group operations.

Covers the representation of Lorentz transformations through general fields and the consequences of symmetry.

Covers Lie groups, Lorentz transformations, boosts, rotations, and complexified Lie algebras.

Explores simple models, electronic structure evaluation, and machine learning at the atomic scale.

Covers singular vectors in Liouville CFT, focusing on representation theory and their implications in mathematical physics.

Explores the Lie theorem and irreducible representations in group theory.

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