Local theta lift for p-adic unitary dual pairs U(2)×U(1) and U(2)×U(3)

Abstract

In this paper we describe the local theta lift for $p$-adic unitary dual pairs $\mathrm{U}\left(2\right)\times \mathrm{U}\left(1\right)$ and $\mathrm{U}\left(2\right)\times \mathrm{U}\left(3\right)$. We also describe the local theta lift for a pair of $p$-adic quaternionic unitary groups of rank $1$.