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

TL;DR

This paper establishes the Plancherel decomposition and relative character identities for a specific symmetric space, leading to a factorization of a global period, advancing understanding of harmonic analysis on this space.

Contribution

It provides the explicit Plancherel decomposition and relative character identities for the space U(2)ackslash SO(2,3), confirming the Sakellaridis-Venkatesh conjecture in this case.

Findings

Explicit Plancherel decomposition for U(2)ackslash SO(2,3)

Derivation of relative character identities

Factorization of the global period P_{U(2)}

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 $P_{U(2)}$.