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arXiv · 0906.4397

Locally compact abelian groups with symplectic self-duality

Amritanshu Prasad·Ilya Shapiro·M. K. Vemuri
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Abstract

Is every locally compact abelian group which admits a symplectic self-duality isomorphic to the product of a locally compact abelian group and its Pontryagin dual? Several sufficient conditions, covering all the typical applications are found. Counterexamples are produced by studying a seemingly unrelated question about the structure of maximal isotropic subgroups of finite abelian groups with symplectic self-duality (where the original question always has an affirmative answer).

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Amritanshu Prasad, Ilya Shapiro, M. K. Vemuri. 2009-06-24. Locally compact abelian groups with symplectic self-duality. https://doi.org/10.1016/j.aim.2010.04.023

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