On the Theta Lift for the Trivial Representation

Abstract

We describe the Howe quotient and theta lift for the trivial representation of $Sp(2n,\mathbb{R})$ for the dual pairs $(O(p,q), Sp(2n,\mathbb{R}))$, within the stable range (i.e., $\min(p, q) \gt 2n$), by explicitly constructing the Howe quotients.