Morphisms 0013 \(\to\) 029N

\(U(2) \to U \oplus U(2)^{2} \oplus D_{4}(-2)\)

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.

\[\left(\begin{array}{rr} 0 & 0 \\ 0 & 0 \\ 1 & 0 \\ 0 & 1 \\ 0 & 0 \\ 0 & 0 \\ 0 & 0 \\ 0 & 0 \\ 0 & 0 \\ 0 & 0 \\ \end{array}\right)\]

{"matrix": [
  [0, 0],
  [0, 0],
  [1, 0],
  [0, 1],
  [0, 0],
  [0, 0],
  [0, 0],
  [0, 0],
  [0, 0],
  [0, 0]
],
 "row_subdivisions": [],
 "column_subdivisions": []}

Diagonal into the summands \(\{2, 3\}\)

A morphism \(U(2)(2) \to U \oplus U(2)^{2} \oplus D_{4}(-2)\): \(b_T(\varphi x, \varphi y) = 2 \, b_S(x, y)\).

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.

\[\left(\begin{array}{rr} 0 & 0 \\ 0 & 0 \\ 1 & 0 \\ 0 & 1 \\ 1 & 0 \\ 0 & 1 \\ 0 & 0 \\ 0 & 0 \\ 0 & 0 \\ 0 & 0 \\ \end{array}\right)\]

{"matrix": [
  [0, 0],
  [0, 0],
  [1, 0],
  [0, 1],
  [1, 0],
  [0, 1],
  [0, 0],
  [0, 0],
  [0, 0],
  [0, 0]
],
 "row_subdivisions": [],
 "column_subdivisions": []}