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arXiv · 1610.07097

Analysis of minimal representations of SL(n,R)

Dehbia Achab
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Abstract

Some 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.

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Dehbia Achab. 2016-10-22. Analysis of minimal representations of SL(n,R). https://arxiv.org/abs/1610.07097

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