We construct new irreducible components in the discrete automorphic spectrum of symplectic groups. The construction lifts a cuspidal automorphic representation of GL2n with a linear period to an irreducible component of the residual spectrum of the rank k symplectic group Spk
Nearby in the stack
for any
k≥2n
. We show that this residual representation admits a non-zero
Spn×Spk−n
-invariant linear form. This generalizes a construction of Ginzburg, Rallis and Soudry, the case