On $p$-refined Friedberg-Jacquet integrals and the classical symplectic locus in the ${\mathrm{GL}}_{2n}$ eigenvariety

Daniel Barrera Salazar, Andrew Graham, Chris Williams

Friedberg--Jacquet proved that if $\pi$ is a cuspidal automorphic representation of ${\mathrm{GL}}_{2n}(\mathbb{A})$, then $\pi$ is a functorial transfer from ${\mathrm{GSpin}}_{2n+1}$ if…