An analogue of Brylinski's knot beta function is defined for a submanifold of d-dimensional Euclidean space. This is a meromorphic function on the complex plane. The first few residues are computed for a surface in three dimensional space.
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).Comment: 23 page
A characterisation of the maximal abelian subalgebras of the bounded operators on Hilbert space that are normalised by the canonical representation of the Heisenberg group is given. This is used to classify the perfect realizations of the canonical representation.
Abstract. A characterization of the maximal abelian sub-algebras of matrix algebras that are normalized by the canonical representation of a finite Heisenberg group is given. Examples are constructed using a classification result for finite Heisenberg groups.
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