Table 8 Weyl group \(D_{4}\), level 3, elements 14–15
From: Extending Snow’s algorithm for computations in the finite Weyl groups
\(N^{o}\) | Weight | Element | Matrix | Inverse |
|---|---|---|---|---|
\(\begin{array}{c} 14 \\ (11) \end{array}\) | 3, 1, −3, 1 | \(\begin{array}{c} s_{3}s_{2}s_{4} \end{array}\) | \( \begin{bmatrix} 1 & 0 & 0 & 0 \\ 1 & 0 & 1 & -1 \\ 1 & 0 & 0 & -1 \\ 0 & 1 & 0 & -1 \end{bmatrix} \) | \(\begin{array}{c} s_{4}s_{2}s_{3} \end{array}\) |
\(\begin{array}{c} 15 \\ (15) \end{array}\) | 3, −1, 3, −1 | \(\begin{array}{c} s_{4}s_{2}s_{4} \end{array}\) | \( \begin{bmatrix} 1 & 0 & 0 & 0 \\ 1 & 0 & 1 & -1 \\ 0 & 0 & 1 & 0 \\ 1 & -1 & 1 & 0 \end{bmatrix} \) | \(\begin{array}{c} s_{4}s_{2}s_{4} \end{array}\) |