Polish groups with ample generics and analytic P-ideals

A Polish group has ample generics if all its diagonal conjugation actions have a comeager orbit. This property has a number of interesting implications, e.g. automatic continuity of homomorphisms into separable groups. Until recently, all known examples of Polish groups with ample generics were non-archimedean, i.e. they were isomorphic to automorphism groups of countable models. I will present a family of Polish groups with ample generics that are not of this form. Their construction uses analytic P-ideals.