| Résume | A locally compact abelian group $L$ is said to have symplectic self-duality if there exists an isomorphism $e:L\rightarrow \hat{L}$ such that $e(x)(x)=0$ for each $x$ in $L$. Is every such group isomorphic to the product of a locally compact abelian group with its Pontryagin dual? What do its maximal isotropic subgroups look like? These questions are motivated by the study of Heisenberg groups and integral transforms that arise from the Stone-von Neumann theorem. We will use a homological method of Fuchs and Hofmann to address these questions. |
