Analysis of the minimal representation of Sp(r,R)
Abstract
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 L2 functions on Rr. 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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