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arXiv:1611.08385 [math.RT]AbstractReferencesReviewsResources

Analysis of the minimal representation of Sp(r,R)

Dehbia Achab

Published 2016-11-25Version 1

The minimal representations of Sp(r,R) can be realized on a Hilbert space of holomorphic functions. This is the analogue of the Brylinski-Kostant model. It can also be realized on a Hilbert space of L^2 functions on R^r. This is the Schr\"oodinger model. We will describe the two realizations and a transformation which maps one model to the other. It involves the classical Bargmann transform and can be seen as its analogue.

Comments: 16 pages. arXiv admin note: text overlap with arXiv:1206.1737
Categories: math.RT
Subjects: 22E46, 17C36
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