An associative algebra of functions on the orbits of nilpotent Lie groups

We introduce an associative bilinear product F * G on the space of Schwartz functions of the coadjoint orbits of a large family of nilpotent Lie groups. We can then introduce an operator , for all . When the nilpotent group is the Heisenberg group N(3), the correspondence is a canonical prequantization of functions F(q, p) in phase space. Part of this work was done at the University of California, Los Angeles.