MSG 84.53

\[\begin{align*} &E_{2}^{1,-1}=0\\ &E_{1}^{0,-1}=\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{D}_1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{D}_2}]\oplus\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{F}_1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{F}_2}]\\ &E_{1}^{1,-1}=\mathbb{Z}[\boldsymbol{b}^{(1)}_{e_1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{g_1}]\\ &E_{1}^{2,-1}=0 \end{align*}\]

\[\begin{align*} &[X^{(1)}]^{-1}=\left( \begin{array}{cc} e_1 & g_1 \\ -1 & 0 \\ 0 & -1 \\ \end{array} \right)\\ &[V^{(0)}]^{-1}=\left( \begin{array}{cccc} \text{D}_1 & \text{D}_2 & \text{F}_1 & \text{F}_2 \\ 1 & 1 & 0 & 0 \\ 0 & 0 & 1 & 1 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ \end{array} \right)\\ &\Lambda^{(0)}=\left( \begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ \end{array} \right) \end{align*} \]