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arXiv:1610.07097 [math.RT]AbstractReferencesReviewsResources

Analysis of the minimal representations of SL(n,R)

Dehbia Achab

Published 2016-10-22Version 1

The minimal representations of SL(n,R) can be realized on a Hilbert space of holomorphic functions. This is the analogue of the Brylinski-Kostant model. They can also be realized on a Hilbert space of homogeneous functions on ${\bboard R}^n$. This is the analogue of the Kobayashi-Orsted model. We will describe the two realizations and a transformation which maps one model to the other. It can be seen as an analogue of the classical Bargmann transform.

Comments: 28 pages. arXiv admin note: text overlap with arXiv:1103.1614
Categories: math.RT
Subjects: 22E46, 17C36
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