Analysis of the minimal representation of Sp(r,R)
arXiv:1611.08385
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 L^2 functions on R^r. This is the Schröodinger 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.
18 pages. arXiv admin note: text overlap with arXiv:1206.1737