Lectures related to Spherical Hecke Algebra: Irreps and Eigenspaces

Explores Schur's lemma and its applications in representations of an associative algebra over an algebraically closed field.

Covers the representation theory of unitary minimal models and the Virasoro algebra.

Explores Wedderburn's theorem, group algebras, and Maschke's theorem in the context of finite dimensional simple algebras and their endomorphisms.

Covers ideals, representations, modules, and maximal ideals in associative algebras.

Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.

Covers the structure of finite dimensional algebras and the characterization of semisimple algebras.

Explores Lie algebras, representations, tensor products, and commutation relations in mathematics.

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

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

Covers the density theorem in representation theory, focusing on endomorphisms of simple finite-dimensional modules.

Covers the complete reducibility of complex representations and the relation between Lie algebras and Lie groups.

Covers the interpretation of the Lindblad equation and its unitary part in quantum gases.

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

Covers the representation theory of groups, focusing on actions and invariants.

Explains the concept of generators of groups and their mathematical properties.

Explores quantum circuit modeling, approximations, unitary matrices, and measurement operations.

Explores identical applications in linear algebra, discussing their representation and implications through examples and equation solving.

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

Covers tensor algebras, symmetric and exterior algebras, and tensor products of modules.

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