On representations of ${\rm GL}_{2n}(F)$ with a symplectic period
  The main aim of this paper is to classify the irreducible admissible representations of ${\rm GL}_{4}(F)$ and ${\rm GL}_{6}(F)$ for a nonarchimedean local field $F$, which bear a nontrivial linear form invariant under the groups ${\rm Sp}_{4}(F)$ and ${\rm Sp}_{6}(F)$ respectively. We propose a few conjectures for the general case. 
Arnab Mitra
math.RT