Analysis of the minimal representation of Sp(r,R)
Representation Theory
2016-12-08 v2
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 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.
Keywords
Cite
@article{arxiv.1611.08385,
title = {Analysis of the minimal representation of Sp(r,R)},
author = {Dehbia Achab},
journal= {arXiv preprint arXiv:1611.08385},
year = {2016}
}
Comments
18 pages. arXiv admin note: text overlap with arXiv:1206.1737