Analysis of the minimal representation of Sp(r,R)
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 an...
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| Sprache: | eng |
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| Zusammenfassung: | 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. |
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| DOI: | 10.48550/arxiv.1611.08385 |