Category OO for the Schrödinger algebra

We study category OO for the (centrally extended) Schrödinger algebra. We determine the quivers for all blocks and relations for blocks of nonzero central charge. We also describe the quiver and relations for the finite dimensional part of OO. We use this to determine the center of the universal enveloping algebra and annihilators of Verma modules. Finally, we classify primitive ideals of the universal enveloping algebra which intersect the center of the centrally extended Schrödinger algebra trivially.