Analysis of minimal representations of SL(n,R)

2016/10/22 by Achab, Dehbia
#17C36 #22E46 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1610.07097

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 Rⁿ. 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.

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