Analysis of the minimal representation of Sp(r,R)

2016/11/25 by Achab, Dehbia
#17C36 #2010 : 22E46 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/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 L² 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.

Related

• Analysis of minimal representations of SL(n,R)
• Special Reduced Multiplets and Minimal Representations for Sp(n,R)
• Analysis of the Brylinski-Kostant model for spherical minimal representations
• Branching laws for minimal holomorphic representations
• Minimal representations of the metaplectic Lie supergroup and the super Segal-Bargmann transform