3.30 p.m. Locally compact abelian groups with symplectic selfduality Amritanshu Prasad Institute of Mathematical Sciences, Chennai. 290409 Abstract A symplectic selfduality of a locally compact abelian group L is an isomorphism f from L onto its Pontryagin dual such that f(x)(x)=0 for all x in L. Groups admitting a symplectic selfduality arise in the context of Heisenberg groups. The following question has been open so far: If L admits a symplectic selfduality then does L have to be isomorphic to the product of a locally compact abelian group and its Pontryagin dual? 1. We describe several classes of groups for which this question has an affirmative answer (covering all typical applications). 2. We study extensions of finite abelian groups to construct a topological torsion group which admits a symplectic selfduality but is not isomorphic to the product of a locally compact abelian group with its Pontryagin dual.
