Table 23 Weyl group \(D_{4}\), level 11, elements 0–3
From: Extending Snow’s algorithm for computations in the finite Weyl groups
\(N^{o}\) | Weight | Element | Matrix | Inverse |
|---|---|---|---|---|
\(\begin{array}{c} 0 \\ (0) \end{array}\) | −1, −2, −1, 1 | \(\begin{array}{c} s_{3}s_{2}s_{4}s_{3}s_{2}s_{1}s_{2}s_{4}s_{3}s_{2}s_{1} \end{array}\) | \( \begin{bmatrix} -1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0 \\ 0 & -1 & 0 & 1 \end{bmatrix} \) | \(\begin{array}{c} s_{3}s_{2}s_{4}s_{3}s_{2}s_{1}s_{2}s_{4}s_{3}s_{2}s_{1} \end{array}\) |
\(\begin{array}{c} 1 \\ (1) \end{array}\) | −1, −2, 1, −1 | \(\begin{array}{c} s_{4}s_{2}s_{4}s_{3}s_{2}s_{1}s_{2}s_{4}s_{3}s_{2}s_{1} \end{array}\) | \( \begin{bmatrix} -1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & -1 & 1 & 0 \\ 0 & 0 & 0 & -1 \end{bmatrix} \) | \(\begin{array}{c} s_{4}s_{2}s_{4}s_{3}s_{2}s_{1}s_{2}s_{4}s_{3}s_{2}s_{1} \end{array}\) |
\(\begin{array}{c} 2 \\ (2) \end{array}\) | −2, 1, −2, −2 | \(\begin{array}{c} s_{4}s_{3}s_{2}s_{4}s_{3}s_{1}s_{2}s_{4}s_{3}s_{2}s_{1} \end{array}\) | \( \begin{bmatrix} -1 & 0 & 0 & 0 \\ -1 & 1 & -1 & -1 \\ 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & -1 \end{bmatrix} \) | \(\begin{array}{c} s_{4}s_{3}s_{2}s_{4}s_{3}s_{1}s_{2}s_{4}s_{3}s_{2}s_{1} \end{array}\) |
\(\begin{array}{c} 3 \\ (3) \end{array}\) | 1, −2, −1, −1 | \(\begin{array}{c} s_{4}s_{3}s_{2}s_{4}s_{3}s_{2}s_{1}s_{2}s_{4}s_{3}s_{2} \end{array}\) | \( \begin{bmatrix} 1 & -1 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & -1 \end{bmatrix} \) | \(\begin{array}{c} s_{4}s_{3}s_{2}s_{4}s_{3}s_{2}s_{1}s_{2}s_{4}s_{3}s_{2} \end{array}\) |