${\mathcal{G}}_6\cong {\mathcal{G}}_2\oplus {\mathcal{G}}_3$

${\mathbb{A}}_1$

${\mathbb{A}}_2$

${\mathbb{A}}_3$

$2{\mathcal{G}}_3={\mathbb{A}}_1\cap {\mathbb{A}}_2\cap {\mathbb{A}}_3$

${\mathbb{B}}_1$

$\mathfrak{L}\left(0,1\right)=\Gamma \left(-1,-1\right)$

$\mathfrak{L}\left(\mathrm{3,2}\right)=\Gamma \left(\mathrm{0,}-1\right)$

$\mathfrak{L}\left(\mathrm{3,1}\right)=\Gamma \left(\mathrm{1,}-1\right)$

$\mathfrak{L}\left(\mathrm{0,2}\right)=\Gamma \left(-1\right)$

${\mathbb{B}}_2$

$\mathfrak{L}\left(2,3\right)=\Gamma \left(-1,0\right)$

$\mathfrak{L}\left(\mathrm{1,0}\right)=\Gamma \left(\mathrm{0,0}\right)$

$\mathfrak{L}\left(\mathrm{1,3}\right)=\Gamma \left(\mathrm{1,0}\right)$

$\mathfrak{L}\left(\mathrm{2,0}\right)=\Gamma \left(0\right)$

${\mathbb{B}}_3$

$\mathfrak{L}\left(2,5\right)=\Gamma \left(-1,2\right)$

$\mathfrak{L}\left(\mathrm{1,4}\right)=\Gamma \left(\mathrm{0,2}\right)$ ,

$\mathfrak{L}\left(\mathrm{1,1}\right)=\Gamma \left(\mathrm{1,2}\right)$

$\mathfrak{L}\left(2,2\right)=\Gamma \left(1\right)$

${\mathbb{B}}_4$

$\mathfrak{L}\left(2,1\right)=\Gamma \left(-1,1\right)$

$\mathfrak{L}\left(1,2\right)=\Gamma \left(0,1\right)$

$\mathfrak{L}\left(\mathrm{1,5}\right)=\Gamma \left(\mathrm{1,1}\right)$

$\mathfrak{L}\left(2,4\right)=\Gamma \left(2\right)$

$3{\mathcal{G}}_2={\mathbb{B}}_1\cap {\mathbb{B}}_2\cap {\mathbb{B}}_3\cap {\mathbb{B}}_4$

$\mathfrak{L}\left(0,3\right)=\Gamma \left(-1\right)$

$\mathfrak{L}\left(3,0\right)=\Gamma \left(0\right)$

$\mathfrak{L}\left(\mathrm{3,3}\right)=\Gamma \left(1\right)$