Abstract
We construct new irreducible components in the discrete automorphic spectrum
of symplectic groups. The construction lifts a cuspidal automorphic
representation of $\mathrm{GL}_{2n}$ with a linear period to an irreducible
component of the residual spectrum of the rank $k$ symplectic group
$\mathrm{Sp}_k$ for any $k\ge 2n$. We show that this residual representation
admits a non-zero $\mathrm{Sp}_n\times \mathrm{Sp}_{k-n}$-invariant linear
form. This generalizes a construction of Ginzburg, Rallis and Soudry, the case
$k=2n$, that arises in the descent method.