Tensor Product of Representations

This lecture explores the concept of the tensor product of representations, showing how combining two spins results in a new particle with a different spin. The discussion delves into the symmetries of a triangle, the group of transformations leaving it invariant, and the irreducible representations of this group. The lecture also covers the classes of conjugation, the number and dimensions of irreducible representations, and the decomposition of matrices in 2D representations. The instructor demonstrates how to write the transformation matrices for rotations and mirrors, and how to decompose them into a 6D representation. The lecture concludes with a practical example involving the molecular structure of ammonia, illustrating the application of symmetry transformations in physics.