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A systematic way to organise the interesting periods of automorphic forms ona reductive group $G$ is via the theory of nilpotent orbits of $G$. On theother hand, it is known that the theta correspondence can be used effectivelyto relate automorphic periods on each member of a dual pair. In this paper, weestablish this relation in full generality, facilitated by a certain transferof nilpotent orbits via moment maps. This is the analogous global result to thelocal result previously established by Gomez and Zhu.

Global theta lifting and automorphic periods associated to nilpotent orbits