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Dimensional upper bounds for admissible subgroups for the metaplectic representation

✍ Scribed by E. Cordero; F. De Mari; K. Nowak; A. Tabacco

Publisher
John Wiley and Sons
Year
2010
Tongue
English
Weight
182 KB
Volume
283
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

We prove dimensional upper bounds for admissible Lie subgroups H of G = ℍ^d^ β‹Š Sp (d, ℝ), d β‰₯ 2. The notion of admissibility captures natural geometric phenomena of the phase space and it is a sufficient condition for a subgroup to be reproducing. It is expressed in terms of absolutely convergent integrals of Wigner distributions, translated by the affine action of the subgroup. We show that dim H ≀ d^2^ + 2__d__, whereas if H βŠ‚ Sp (d, R), then dim H ≀ d^2^ + 1. Both bounds are shown to be optimal (Β© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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