$\mathrm{codim}\Sigma$	Z	$Z=\widehat{S}/\widehat{H}$	Y	Real form of $\widehat{S}$
1	${\mathbb{P}}_1$	${\mathrm{SL}}_2(\mathbb{C})/B_1$	$S^1$	${\mathrm{SL}}_2(\mathbb{R})$
2	${\mathbb{P}}_1\times {\mathbb{P}}_1$	${\mathrm{SL}}_2(\mathbb{C})\times {\mathrm{SL}}_2(\mathbb{C})/B_1\times B_2$	$S^1\times S^1$	${\mathrm{SL}}_2(\mathbb{R})\times {\mathrm{SL}}_2(\mathbb{R})$
2	${\mathbb{P}}_1\times {\mathbb{P}}_1$	${\mathrm{SL}}_2(\mathbb{C})\times {\mathrm{SL}}_2(\mathbb{C})/B_1\times B_2$	${\mathcal{M}}_1$	${\mathrm{SL}}_2(\mathbb{C})$
2	${\mathbb{P}}_2$	${\mathrm{SL}}_3(\mathbb{C})/P$	${\mathbb{RP}}_2$	${\mathrm{SL}}_3(\mathbb{R})$
2	$Q_{[2]}$	${\mathrm{SL}}_2(\mathbb{C})/{\mathbb{C}}^{\ast }$	$S^2$	$\mathrm{SU}(2)$
2	${\mathbb{P}}_2\backslash C$	${\mathrm{SL}}_2(\mathbb{C})/{\mathbb{Z}}_2{\mathbb{C}}^{\ast }$	${\mathbb{RP}}_2$	$\mathrm{SU}(2)$