The Sakellaridis-Venkatesh Conjecture for $ U(2)\backslash SO_{2,3}$

Abstract

This article gives the Plancherel decomposition of $L^2\left(U(2)(F)\backslash SO_{2,3}(F)\right)$, where $F$ is a local field with characteristic $0$, and the relative character identities. Finally, we obtain a factorization of the global period $P_{U(2)}$.