Table 5 Weyl group \(D_{4}\), level 1, elements 0–3
From: Extending Snow’s algorithm for computations in the finite Weyl groups
\(N^{o}\) | Weight | Element | Matrix | \(N^{o}\) | Weight | Element | Matrix |
|---|---|---|---|---|---|---|---|
0 | −1, 2, 1, 1 | \(s_{1}\) | \( \begin{bmatrix} -1 & 1 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix} \) | 1 | 2, −1, 2, 2 | \(s_{2}\) | \( \begin{bmatrix} 1 & 0 & 0 & 0 \\ 1 & -1 & 1 & 1 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix} \) |
2 | 1, 2, −1, 1 | \(s_{3}\) | \( \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 1 & -1 & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix} \) | 3 | 1, 2, 1, −1 | \(s_{4}\) | \( \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & -1 \end{bmatrix} \) |