Regular Weyl-Systems and Smooth Structures on Heisenberg Groups |
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Authors: | Günther Hörmann |
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Institution: | Institut für Mathematik, Universit?t Wien, Wien, Austria. Email: gue@cma.univie.ac.at, AU
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Abstract: | We study representation theory of the Weyl relations for infinitely many degrees of freedom. Differentiability of regular
representations along rays in the parameter space E suggests to consider smooth structures on E. Switching from representations of CCR to group representations of the associated Heisenberg group over E we develop a framework for smooth representations of the Heisenberg group as an infinite dimensional Lie group. After careful
inspection and translation of the necessary differential geometric input for Kirillov's orbit method we are able to construct
a large class of smooth representations. These reproduce the Schr?dinger representation if E is finite dimensional.
Received: 10 May 1996 / Accepted: 30 July 1996 |
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