Analysis of minimal representations of SL(n,R)

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.

25 pages. arXiv admin note: text overlap with arXiv:1103.1614

References in corpus (2)

• Fock model and Segal-Bargmann transform for minimal representations of Hermitian Lie groups
• Minimal representations of simple real Lie groups of Hermitian type