|XXVIII Workshop on Geometric Methods in Physics||28.06-04.07.2009|
Magnetic Weyl calculus on coadjoint orbits of some infinite-dimensional Lie groups
The talk will report on joint work with Ingrid Beltita.
We develop a Weyl calculus for pseudo-differential operators on nilpotent Lie groups that takes into account magnetic fields on the groups under consideration. To this end we use an infinite-dimensional Lie group constructed as the semidirect product of a nilpotent Lie group and an appropriate function space thereon. We single out an appropriate coadjoint orbit of that semidirect product and construct our pseudo-differential calculus as a Weyl quantization of that orbit. In the case when the nilpotent group is the additive group of some finite-dimensional vector space, we recover some known properties of the magnetic pseudo-differential calculus that has been recently constructed.