Minimal representations of simple real Lie groups of non Hermitian type

TL;DR

This paper extends previous work on minimal representations of simple real Lie groups of non Hermitian type, providing a unified geometric realization for a family of their unitary irreducible representations.

Contribution

It generalizes the Brylinski-Kostant model analysis and offers a new unified geometric framework for these representations.

Findings

Unified geometric realization of representations

Extension of Brylinski-Kostant model analysis

Framework applicable to non Hermitian type groups

Abstract

In the recent paper [AF12], we introduced an analysis of the Brylinski-Kostant model for spherical minimal representations for simple real Lie groups of non Hermitian type. We generalize here that analysis and give a unified geometric realization to a family of unitary irreducible representations of such groups.