Heisenberg Pairs on Hilbert C*-modules

Lara Ismert
Embry-Riddle Aeronautical University

Roughly speaking, a Heisenberg pair on a Hilbert space is a pair of self-adjoint operators (A,B) which satisfy the Heisenberg Commutation Relation: [A,B]=i. It is well known that at least one of the two operators must be unbounded, which introduces domain challenges in classifying such pairs. A common strategy to work around this challenge is to find sufficient conditions for when the corresponding unitary groups for the Heisenberg pair form a Heisenberg representation. One may then apply the Stone-von Neumann Theorem to yield a uniqueness statement for the Heisenberg pair. In this talk, we discuss an integration strategy on Hilbert C*-modules and a Covariant Stone-von Neumann Theorem which extends the classical one. This is joint work with Leonard Huang.

Presentation (PDF File)

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