\(\langle 2 \rangle \to E_{8} \oplus A_{1}\)
Column \(j\) of each matrix gives \(\varphi(e_j)\) in the chosen basis of the target; the subdivisions separate orthogonal summands of the source (columns) and of the target (rows).
Notes
The embeddings of latticedb.summands: each summand of
the source maps by \(x \mapsto (x, \ldots,
x)\) into a set of orthogonal summands of the target.
Diagonal into the summands \(\{2\}\)
Summand \(j\) of the source maps by \(x \mapsto (x, \ldots, x)\) into the orthogonal summands of the target in set \(j\), which are counted from 1 in the order of the basis.
\[\left(\begin{array}{r}
0 \\
0 \\
0 \\
0 \\
0 \\
0 \\
0 \\
0 \\
1 \\
\end{array}\right)\]
{"matrix": [
[0],
[0],
[0],
[0],
[0],
[0],
[0],
[0],
[1]
],
"row_subdivisions": [],
"column_subdivisions": []}