THE STONE-VON NEUMANN THEOREM FOR LOCALLY COMPACT QUANTUM GROUPS

The Stone-von Neumann theorem rigorously shows the equivalence between two fundamental approaches to quantum mechanics, notably, the matrix mechanics of Heisenberg and the wave mechanics of Schrödinger. This theorem was formulated by Mackey as a theorem about certain unitary representations of locally compact abelian groups. In my talk, based on Rieffel’s proof of Mackey’s theorem, I will present the Stone-von Neumann-type theorem in the setting of locally compact quantum groups in the sense of Woronowicz. Based on joint work with L. Hall, L. Huang, and J. Krajczok.