On the irreducible action of \(\mathrm{PSL}(2, \mathbb{R})\) on the 3-dimensional Einstein universe (Q1681549)

The author studies the irreducible representation of \(\mathrm{PSL} (2, \mathbb{R})\) in \(\mathrm{PSL} (5, \mathbb{R})\). This action preserves a quadratic form with signature \((2,3)\), thus it acts conformally on the 3-dimensional Einstein universe \(\mathbb{E}in^{1,2}\). He describes the orbits induced in \(\mathbb{E}in^{1,2}\) and its complement in \(R\mathbb{P}^4\).