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.
Categories: math.NT math.RT