Weil Representation and Heis Operators

This lecture covers the Weil representation and Heis operators, introducing the Stone-Neumann theorem and the unitary representation of Heis operators. It discusses the action of Heis operators on functions and their Lie algebra structure, emphasizing the importance of the Stone-von Neumann theorem. The lecture also explores the concept of unitary operators and their representation in the context of Heis operators, highlighting the Lie algebra structure and the symplectic form. Additionally, it delves into the co-adjoint realization and the natural action of Heis operators, providing insights into the Lie algebra homomorphism and the canonical map.