On vector-valued automorphic forms on bounded symmetric domains

Abstract

We prove a spanning result for vector-valued Poincaré series on a bounded symmetric domain. We associate a sequence of holomorphic automorphic forms to a submanifold of the domain. When the domain is the unit ball in C n , we provide estimates for the norms of these automorphic forms and we find asymptotics of the norms (as the weight goes to infinity) for a class of totally real submanifolds. We give an example of a CR submanifold of the ball, for which the norms of the associated automorphic forms have a different asymptotic behaviour.MSC 2010: 32N15, 53C99

Kähler quantization and entanglement

“…Associating semiclassical states to Lagrangian submanifolds of a symplectic manifold is an idea that arises in many contexts. A partial list of references where various versions of this appear includes [5,8,10,12,17,20,25] and three papers (co-)authored by the first author of this paper: [2,15,16].…”