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A new proof of N. J. Young's theorem on the orbits of the action of the symplectic group

Published online by Cambridge University Press:  20 January 2009

Dan Timotin
Dan Timotin
Affiliation:
Institute of Mathematics of the Romanian Academy, P.O. Box 1–764, Bucharest 70700, Romania
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Abstract

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The group of symplectic transformations acts on the unit ball of a Hilbert space. The structure of the orbits has been determined by N. J. Young in [8]. We provide a new proof of this theorem; it is slightly simpler than the original one, and does not involve Brown–Douglas–Fillmore theory. Moreover, the steps followed hopefully throw some additional light on the subject. We rely heavily on previous work of Khatskevich, Shmulyan and Shulman ([5, 6, 7[); the proofs of the results used are included for completeness.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 40 , Issue 2 , June 1997 , pp. 309 - 315
Copyright
Copyright © Edinburgh Mathematical Society 1997

References

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