qr211

【第2章】対称群 \(S_4\)

⇦ \(\quad \)
home \(\quad \)
⇨

【2-14】 \(S_4\) の既約表現のまとめ

前節で求めた \(\widetilde{L_i}\) は(24x24)と巨大な行列の為すべてを表示できませんが、既約分解された行列の各表現における小行列を抽出して、そのすべてを 記述することはできます。以下がその表となります。何かの参考になれば幸いです。

\begin{align} & \widetilde{L_i}= \begin{bmatrix} \boxed{\rho_{1}}&0&0&0&0&0&0&0&0&0 \\ 0&\boxed{ \rho_{2} }&0&0&0&0&0&0&0&0&\\ 0&0& \boxed{ \begin{matrix} 2 \times 2 \\ \rho_{3,1} \end{matrix}}&0&0&0&0&0&0&0\\ 0&0&0&\boxed{ \begin{matrix} 2 \times 2 \\ \rho_{3,2} \end{matrix}} &0&0&0&0&0&0 \\ 0&0&0&0& \boxed{ \begin{matrix} 3 \times 3 \\ \rho_{4,1} \end{matrix}} &0&0&0&0&0 \\ 0&0&0&0&0& \boxed{ \begin{matrix} 3 \times 3 \\ \rho_{4,2} \end{matrix}} &0&0&0&0 \\ 0&0&0&0&0&0& \boxed{ \begin{matrix} 3 \times 3 \\ \rho_{4,3} \end{matrix}} &0&0&0 \\ 0&0&0&0&0&0&0& \boxed{ \begin{matrix} 3 \times 3 \\ \rho_{5,1} \end{matrix}}&0&0 \\ 0&0&0&0&0&0&0&0& \boxed{ \begin{matrix} 3 \times 3 \\ \rho_{5,2} \end{matrix}} &0 \\ 0&0&0&0&0&0&0&0&0& \boxed{ \begin{matrix} 3 \times 3 \\ \rho_{5,3} \end{matrix}}\\ \end{bmatrix}\\ \notag \\ \end{align}


【表4】\(S_4\) の既約表現
\(S_4\) の元\(\sigma_{1}\)\(\sigma_{2}\)\(\sigma_{3}\)\(\sigma_{4}\)\(\sigma_{5}\)\(\sigma_{6}\)
巡回表現\( e\)\( (34) \)\( (23) \)\( (24) \)\( (12) \)\( (13) \)
\(\rho_{1}\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(\rho_{2}\)\(1\)\(-1\)\(-1\)\(-1\)\(-1\)\(-1\)
\(\rho_{3,1}\)\(\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}\)\(\begin{bmatrix}0 & 1\\1 & 0\end{bmatrix}\)\(\begin{bmatrix}1 & 0\\-1 & -1\end{bmatrix}\) \(\begin{bmatrix}-1 & -1\\0 & 1\end{bmatrix}\)\(\begin{bmatrix}0 & 1\\1 & 0\end{bmatrix}\)\(\begin{bmatrix}-1 & -1\\0 & 1\end{bmatrix}\)
\(\rho_{3,2}\)\(\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}\)\(\begin{bmatrix}-1 & -1\\0 & 1\end{bmatrix}\)\(\begin{bmatrix}1 & 0\\-1 & -1\end{bmatrix}\) \(\begin{bmatrix}0 & 1\\1 & 0\end{bmatrix}\)\(\begin{bmatrix}-1 & -1\\0 & 1\end{bmatrix}\)\(\begin{bmatrix}0 & 1\\1 & 0\end{bmatrix}\)
\(\rho_{4,1}\)\(\begin{bmatrix}1 & 0 & 0\\0 & 1 & 0\\0 & 0 & 1\end{bmatrix}\)\(\begin{bmatrix}-1 & -1 & -1\\0 & 1 & 0\\0 & 0 & 1\end{bmatrix}\) \(\begin{bmatrix}1 & 0 & 0\\0 & 1 & 0\\-1 & -1 & -1\end{bmatrix}\)\(\begin{bmatrix}0 & 0 & 1\\0 & 1 & 0\\1 & 0 & 0\end{bmatrix}\) \(\begin{bmatrix}1 & 0 & 0\\0 & 0 & 1\\0 & 1 & 0\end{bmatrix}\)\(\begin{bmatrix}1 & 0 & 0\\-1 & -1 & -1\\0 & 0 & 1\end{bmatrix}\)
\(\rho_{4,2}\)\(\begin{bmatrix}1 & 0 & 0\\0 & 1 & 0\\0 & 0 & 1\end{bmatrix}\)\(\begin{bmatrix}1 & 0 & 0\\0 & 0 & 1\\0 & 1 & 0\end{bmatrix}\) \(\begin{bmatrix}0 & 1 & 0\\1 & 0 & 0\\0 & 0 & 1\end{bmatrix}\)\(\begin{bmatrix}0 & 0 & 1\\0 & 1 & 0\\1 & 0 & 0\end{bmatrix}\) \(\begin{bmatrix}-1 & -1 & -1\\0 & 1 & 0\\0 & 0 & 1\end{bmatrix}\)\(\begin{bmatrix}1 & 0 & 0\\-1 & -1 & -1\\0 & 0 & 1\end{bmatrix}\)
\(\rho_{4,3}\)\(\begin{bmatrix}1 & 0 & 0\\0 & 1 & 0\\0 & 0 & 1\end{bmatrix}\)\(\begin{bmatrix}0 & 1 & 0\\1 & 0 & 0\\0 & 0 & 1\end{bmatrix}\) \(\begin{bmatrix}0 & 0 & -1\\0 & 1 & 0\\-1 & 0 & 0\end{bmatrix}\)\(\begin{bmatrix}1 & 0 & 0\\0 & 0 & -1\\0 & -1 & 0\end{bmatrix}\) \(\begin{bmatrix}0 & -1 & 0\\-1 & 0 & 0\\0 & 0 & 1\end{bmatrix}\)\(\begin{bmatrix}1 & 0 & 0\\0 & 0 & 1\\0 & 1 & 0\end{bmatrix}\)
\(\rho_{5,1}\)\(\begin{bmatrix}1 & 0 & 0\\0 & 1 & 0\\0 & 0 & 1\end{bmatrix}\)\(\begin{bmatrix}1 & 1 & 1\\0 & -1 & 0\\0 & 0 & -1\end{bmatrix}\) \(\begin{bmatrix}-1 & 0 & 0\\0 & -1 & 0\\1 & 1 & 1\end{bmatrix}\)\(\begin{bmatrix}0 & 0 & -1\\0 & -1 & 0\\-1 & 0 & 0\end{bmatrix}\) \(\begin{bmatrix}-1 & 0 & 0\\0 & 0 & -1\\0 & -1 & 0\end{bmatrix}\)\(\begin{bmatrix}-1 & 0 & 0\\1 & 1 & 1\\0 & 0 & -1\end{bmatrix}\)
\(\rho_{5,2}\)\(\begin{bmatrix}1 & 0 & 0\\0 & 1 & 0\\0 & 0 & 1\end{bmatrix}\)\(\begin{bmatrix}-1 & 0 & 0\\0 & 0 & -1\\0 & -1 & 0\end{bmatrix}\) \(\begin{bmatrix}0 & -1 & 0\\-1 & 0 & 0\\0 & 0 & -1\end{bmatrix}\)\(\begin{bmatrix}0 & 0 & -1\\0 & -1 & 0\\-1 & 0 & 0\end{bmatrix}\) \(\begin{bmatrix}1 & 1 & 1\\0 & -1 & 0\\0 & 0 & -1\end{bmatrix}\)\(\begin{bmatrix}-1 & 0 & 0\\1 & 1 & 1\\0 & 0 & -1\end{bmatrix}\)
\(\rho_{5,3}\)\(\begin{bmatrix}1 & 0 & 0\\0 & 1 & 0\\0 & 0 & 1\end{bmatrix}\)\(\begin{bmatrix}-1 & 0 & 0\\0 & 0 & -1\\0 & -1 & 0\end{bmatrix}\) \(\begin{bmatrix}0 & -1 & 0\\-1 & 0 & 0\\0 & 0 & -1\end{bmatrix}\)\(\begin{bmatrix}0 & 0 & -1\\0 & -1 & 0\\-1 & 0 & 0\end{bmatrix}\) \(\begin{bmatrix}-1 & 0 & 0\\0 & 0 & 1\\0 & 1 & 0\end{bmatrix}\)\(\begin{bmatrix}0 & 0 & 1\\0 & -1 & 0\\1 & 0 & 0\end{bmatrix}\)

\(S_4\) の元\(\sigma_{7}\)\(\sigma_{8}\)\(\sigma_{9}\)\(\sigma_{10}\)\(\sigma_{11}\)\(\sigma_{12}\)
巡回表現\( (14) \)\( (234) \)\( (243) \)\( (123) \)\( (124) \)\( (132) \)
\(\rho_{1}\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(\rho_{2}\)\(-1\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(\rho_{3,1}\)\(\begin{bmatrix}1 & 0\\-1 & -1\end{bmatrix}\)\(\begin{bmatrix}0 & 1\\-1 & -1\end{bmatrix}\)\(\begin{bmatrix}-1 & -1\\1 & 0\end{bmatrix}\) \(\begin{bmatrix}-1 & -1\\1 & 0\end{bmatrix}\)\(\begin{bmatrix}0 & 1\\-1 & -1\end{bmatrix}\)\(\begin{bmatrix}0 & 1\\-1 & -1\end{bmatrix}\)
\(\rho_{3,2}\)\(\begin{bmatrix}1 & 0\\-1 & -1\end{bmatrix}\)\(\begin{bmatrix}-1 & -1\\1 & 0\end{bmatrix}\)\(\begin{bmatrix}0 & 1\\-1 & -1\end{bmatrix}\) \(\begin{bmatrix}0 & 1\\-1 & -1\end{bmatrix}\)\(\begin{bmatrix}-1 & -1\\1 & 0\end{bmatrix}\)\(\begin{bmatrix}-1 & -1\\1 & 0\end{bmatrix}\)
\(\rho_{4,1}\)\(\begin{bmatrix}0 & 1 & 0\\1 & 0 & 0\\0 & 0 & 1\end{bmatrix}\)\(\begin{bmatrix}-1 & -1 & -1\\0 & 1 & 0\\1 & 0 & 0\end{bmatrix}\) \(\begin{bmatrix}0 & 0 & 1\\0 & 1 & 0\\-1 & -1 & -1\end{bmatrix}\)\(\begin{bmatrix}1 & 0 & 0\\-1 & -1 & -1\\0 & 1 & 0\end{bmatrix}\) \(\begin{bmatrix}0 & 0 & 1\\1 & 0 & 0\\0 & 1 & 0\end{bmatrix}\)\(\begin{bmatrix}1 & 0 & 0\\0 & 0 & 1\\-1 & -1 & -1\end{bmatrix}\)
\(\rho_{4,2}\)\(\begin{bmatrix}1 & 0 & 0\\0 & 1 & 0\\-1 & -1 & -1\end{bmatrix}\)\(\begin{bmatrix}0 & 0 & 1\\1 & 0 & 0\\0 & 1 & 0\end{bmatrix}\) \(\begin{bmatrix}0 & 1 & 0\\0 & 0 & 1\\1 & 0 & 0\end{bmatrix}\)\(\begin{bmatrix}-1 & -1 & -1\\1 & 0 & 0\\0 & 0 & 1\end{bmatrix}\) \(\begin{bmatrix}-1 & -1 & -1\\0 & 1 & 0\\1 & 0 & 0\end{bmatrix}\)\(\begin{bmatrix}0 & 1 & 0\\-1 & -1 & -1\\0 & 0 & 1\end{bmatrix}\)
\(\rho_{4,3}\)\(\begin{bmatrix}0 & 0 & 1\\0 & 1 & 0\\1 & 0 & 0\end{bmatrix}\)\(\begin{bmatrix}0 & 0 & -1\\1 & 0 & 0\\0 & -1 & 0\end{bmatrix}\) \(\begin{bmatrix}0 & 1 & 0\\0 & 0 & -1\\-1 & 0 & 0\end{bmatrix}\)\(\begin{bmatrix}0 & -1 & 0\\0 & 0 & 1\\-1 & 0 & 0\end{bmatrix}\) \(\begin{bmatrix}0 & 0 & 1\\-1 & 0 & 0\\0 & -1 & 0\end{bmatrix}\)\(\begin{bmatrix}0 & 0 & -1\\-1 & 0 & 0\\0 & 1 & 0\end{bmatrix}\)
\(\rho_{5,1}\)\(\begin{bmatrix}0 & -1 & 0\\-1 & 0 & 0\\0 & 0 & -1\end{bmatrix}\)\(\begin{bmatrix}-1 & -1 & -1\\0 & 1 & 0\\1 & 0 & 0\end{bmatrix}\) \(\begin{bmatrix}0 & 0 & 1\\0 & 1 & 0\\-1 & -1 & -1\end{bmatrix}\)\(\begin{bmatrix}1 & 0 & 0\\-1 & -1 & -1\\0 & 1 & 0\end{bmatrix}\) \(\begin{bmatrix}0 & 0 & 1\\1 & 0 & 0\\0 & 1 & 0\end{bmatrix}\)\(\begin{bmatrix}1 & 0 & 0\\0 & 0 & 1\\-1 & -1 & -1\end{bmatrix}\)
\(\rho_{5,2}\)\(\begin{bmatrix}-1 & 0 & 0\\0 & -1 & 0\\1 & 1 & 1\end{bmatrix}\)\(\begin{bmatrix}0 & 0 & 1\\1 & 0 & 0\\0 & 1 & 0\end{bmatrix}\) \(\begin{bmatrix}0 & 1 & 0\\0 & 0 & 1\\1 & 0 & 0\end{bmatrix}\)\(\begin{bmatrix}-1 & -1 & -1\\1 & 0 & 0\\0 & 0 & 1\end{bmatrix}\) \(\begin{bmatrix}-1 & -1 & -1\\0 & 1 & 0\\1 & 0 & 0\end{bmatrix}\)\(\begin{bmatrix}0 & 1 & 0\\-1 & -1 & -1\\0 & 0 & 1\end{bmatrix}\)
\(\rho_{5,3}\)\(\begin{bmatrix}0 & 1 & 0\\1 & 0 & 0\\0 & 0 & -1\end{bmatrix}\)\(\begin{bmatrix}0 & 0 & 1\\1 & 0 & 0\\0 & 1 & 0\end{bmatrix}\) \(\begin{bmatrix}0 & 1 & 0\\0 & 0 & 1\\1 & 0 & 0\end{bmatrix}\)\(\begin{bmatrix}0 & 1 & 0\\0 & 0 & -1\\-1 & 0 & 0\end{bmatrix}\) \(\begin{bmatrix}0 & 0 & 1\\-1 & 0 & 0\\0 & -1 & 0\end{bmatrix}\)\(\begin{bmatrix}0 & 0 & -1\\1 & 0 & 0\\0 & -1 & 0\end{bmatrix}\)

\(S_4\) の元\(\sigma_{13}\)\(\sigma_{14}\)\(\sigma_{15}\)\(\sigma_{16}\)\(\sigma_{17}\)\(\sigma_{18}\)
巡回表現\( (134) \)\( (142) \)\( (143) \)\( (1234) \)\( (1243) \)\( (1342) \)
\(\rho_{1}\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(\rho_{2}\)\(1\)\(1\)\(1\)\(-1\)\(-1\)\(-1\)
\(\rho_{3,1}\)\(\begin{bmatrix}-1 & -1\\1 & 0\end{bmatrix}\)\(\begin{bmatrix}-1 & -1\\1 & 0\end{bmatrix}\)\(\begin{bmatrix}0 & 1\\-1 & -1\end{bmatrix}\) \(\begin{bmatrix}-1 & -1\\0 & 1\end{bmatrix}\)\(\begin{bmatrix}1 & 0\\-1 & -1\end{bmatrix}\)\(\begin{bmatrix}1 & 0\\-1 & -1\end{bmatrix}\)
\(\rho_{3,2}\)\(\begin{bmatrix}0 & 1\\-1 & -1\end{bmatrix}\)\(\begin{bmatrix}0 & 1\\-1 & -1\end{bmatrix}\)\(\begin{bmatrix}-1 & -1\\1 & 0\end{bmatrix}\) \(\begin{bmatrix}0 & 1\\1 & 0\end{bmatrix}\)\(\begin{bmatrix}1 & 0\\-1 & -1\end{bmatrix}\)\(\begin{bmatrix}1 & 0\\-1 & -1\end{bmatrix}\)
\(\rho_{4,1}\)\(\begin{bmatrix}-1 & -1 & -1\\1 & 0 & 0\\0 & 0 & 1\end{bmatrix}\)\(\begin{bmatrix}0 & 1 & 0\\0 & 0 & 1\\1 & 0 & 0\end{bmatrix}\) \(\begin{bmatrix}0 & 1 & 0\\-1 & -1 & -1\\0 & 0 & 1\end{bmatrix}\)\(\begin{bmatrix}-1 & -1 & -1\\1 & 0 & 0\\0 & 1 & 0\end{bmatrix}\) \(\begin{bmatrix}0 & 0 & 1\\-1 & -1 & -1\\0 & 1 & 0\end{bmatrix}\)\(\begin{bmatrix}-1 & -1 & -1\\0 & 0 & 1\\1 & 0 & 0\end{bmatrix}\)
\(\rho_{4,2}\)\(\begin{bmatrix}1 & 0 & 0\\-1 & -1 & -1\\0 & 1 & 0\end{bmatrix}\)\(\begin{bmatrix}0 & 0 & 1\\0 & 1 & 0\\-1 & -1 & -1\end{bmatrix}\) \(\begin{bmatrix}1 & 0 & 0\\0 & 0 & 1\\-1 & -1 & -1\end{bmatrix}\)\(\begin{bmatrix}-1 & -1 & -1\\1 & 0 & 0\\0 & 1 & 0\end{bmatrix}\) \(\begin{bmatrix}-1 & -1 & -1\\0 & 0 & 1\\1 & 0 & 0\end{bmatrix}\)\(\begin{bmatrix}0 & 0 & 1\\-1 & -1 & -1\\0 & 1 & 0\end{bmatrix}\)
\(\rho_{4,3}\)\(\begin{bmatrix}0 & 1 & 0\\0 & 0 & 1\\1 & 0 & 0\end{bmatrix}\)\(\begin{bmatrix}0 & -1 & 0\\0 & 0 & -1\\1 & 0 & 0\end{bmatrix}\) \(\begin{bmatrix}0 & 0 & 1\\1 & 0 & 0\\0 & 1 & 0\end{bmatrix}\)\(\begin{bmatrix}-1 & 0 & 0\\0 & 0 & 1\\0 & -1 & 0\end{bmatrix}\) \(\begin{bmatrix}0 & 0 & 1\\0 & -1 & 0\\-1 & 0 & 0\end{bmatrix}\)\(\begin{bmatrix}0 & 0 & -1\\0 & -1 & 0\\1 & 0 & 0\end{bmatrix}\)
\(\rho_{5,1}\)\(\begin{bmatrix}-1 & -1 & -1\\1 & 0 & 0\\0 & 0 & 1\end{bmatrix}\)\(\begin{bmatrix}0 & 1 & 0\\0 & 0 & 1\\1 & 0 & 0\end{bmatrix}\) \(\begin{bmatrix}0 & 1 & 0\\-1 & -1 & -1\\0 & 0 & 1\end{bmatrix}\)\(\begin{bmatrix}1 & 1 & 1\\-1 & 0 & 0\\0 & -1 & 0\end{bmatrix}\) \(\begin{bmatrix}0 & 0 & -1\\1 & 1 & 1\\0 & -1 & 0\end{bmatrix}\)\(\begin{bmatrix}1 & 1 & 1\\0 & 0 & -1\\-1 & 0 & 0\end{bmatrix}\)
\(\rho_{5,2}\)\(\begin{bmatrix}1 & 0 & 0\\-1 & -1 & -1\\0 & 1 & 0\end{bmatrix}\)\(\begin{bmatrix}0 & 0 & 1\\0 & 1 & 0\\-1 & -1 & -1\end{bmatrix}\) \(\begin{bmatrix}1 & 0 & 0\\0 & 0 & 1\\-1 & -1 & -1\end{bmatrix}\)\(\begin{bmatrix}1 & 1 & 1\\-1 & 0 & 0\\0 & -1 & 0\end{bmatrix}\) \(\begin{bmatrix}1 & 1 & 1\\0 & 0 & -1\\-1 & 0 & 0\end{bmatrix}\)\(\begin{bmatrix}0 & 0 & -1\\1 & 1 & 1\\0 & -1 & 0\end{bmatrix}\)
\(\rho_{5,3}\)\(\begin{bmatrix}0 & -1 & 0\\0 & 0 & 1\\-1 & 0 & 0\end{bmatrix}\)\(\begin{bmatrix}0 & -1 & 0\\0 & 0 & -1\\1 & 0 & 0\end{bmatrix}\) \(\begin{bmatrix}0 & 0 & -1\\-1 & 0 & 0\\0 & 1 & 0\end{bmatrix}\)\(\begin{bmatrix}0 & 0 & -1\\0 & 1 & 0\\1 & 0 & 0\end{bmatrix}\) \(\begin{bmatrix}0 & -1 & 0\\1 & 0 & 0\\0 & 0 & 1\end{bmatrix}\)\(\begin{bmatrix}0 & 1 & 0\\-1 & 0 & 0\\0 & 0 & 1\end{bmatrix}\)

\(S_4\) の元\(\sigma_{19}\)\(\sigma_{20}\)\(\sigma_{21}\)\(\sigma_{22}\)\(\sigma_{23}\)\(\sigma_{24}\)
巡回表現\( (1324) \)\( (1432) \)\( (1423) \)\( (12)(34) \)\( (13)(24) \)\( (14)(23) \)
\(\rho_{1}\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(\rho_{2}\)\(-1\)\(-1\)\(-1\)\(1\)\(1\)\(1\)
\(\rho_{3,1}\) \(\begin{bmatrix}0 & 1\\1 & 0\end{bmatrix}\)\(\begin{bmatrix}-1 & -1\\0 & 1\end{bmatrix}\)\(\begin{bmatrix}0 & 1\\1 & 0\end{bmatrix}\) \(\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}\)\(\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}\)\(\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}\)
\(\rho_{3,2}\)\(\begin{bmatrix}-1 & -1\\0 & 1\end{bmatrix}\)\(\begin{bmatrix}0 & 1\\1 & 0\end{bmatrix}\)\(\begin{bmatrix}-1 & -1\\0 & 1\end{bmatrix}\) \(\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}\)\(\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}\)\(\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}\)
\(\rho_{4,1}\)\(\begin{bmatrix}0 & 0 & 1\\1 & 0 & 0\\-1 & -1 & -1\end{bmatrix}\)\(\begin{bmatrix}0 & 1 & 0\\0 & 0 & 1\\-1 & -1 & -1\end{bmatrix}\) \(\begin{bmatrix}0 & 1 & 0\\-1 & -1 & -1\\1 & 0 & 0\end{bmatrix}\)\(\begin{bmatrix}-1 & -1 & -1\\0 & 0 & 1\\0 & 1 & 0\end{bmatrix}\) \(\begin{bmatrix}0 & 0 & 1\\-1 & -1 & -1\\1 & 0 & 0\end{bmatrix}\)\(\begin{bmatrix}0 & 1 & 0\\1 & 0 & 0\\-1 & -1 & -1\end{bmatrix}\)
\(\rho_{4,2}\)\(\begin{bmatrix}0 & 1 & 0\\-1 & -1 & -1\\1 & 0 & 0\end{bmatrix}\)\(\begin{bmatrix}0 & 1 & 0\\0 & 0 & 1\\-1 & -1 & -1\end{bmatrix}\) \(\begin{bmatrix}0 & 0 & 1\\1 & 0 & 0\\-1 & -1 & -1\end{bmatrix}\)\(\begin{bmatrix}-1 & -1 & -1\\0 & 0 & 1\\0 & 1 & 0\end{bmatrix}\) \(\begin{bmatrix}0 & 0 & 1\\-1 & -1 & -1\\1 & 0 & 0\end{bmatrix}\)\(\begin{bmatrix}0 & 1 & 0\\1 & 0 & 0\\-1 & -1 & -1\end{bmatrix}\)
\(\rho_{4,3}\)\(\begin{bmatrix}0 & 1 & 0\\-1 & 0 & 0\\0 & 0 & -1\end{bmatrix}\)\(\begin{bmatrix}-1 & 0 & 0\\0 & 0 & -1\\0 & 1 & 0\end{bmatrix}\) \(\begin{bmatrix}0 & -1 & 0\\1 & 0 & 0\\0 & 0 & -1\end{bmatrix}\)\(\begin{bmatrix}-1 & 0 & 0\\0 & -1 & 0\\0 & 0 & 1\end{bmatrix}\) \(\begin{bmatrix}1 & 0 & 0\\0 & -1 & 0\\0 & 0 & -1\end{bmatrix}\)\(\begin{bmatrix}-1 & 0 & 0\\0 & 1 & 0\\0 & 0 & -1\end{bmatrix}\)
\(\rho_{5,1}\)\(\begin{bmatrix}0 & 0 & -1\\-1 & 0 & 0\\1 & 1 & 1\end{bmatrix}\)\(\begin{bmatrix}0 & -1 & 0\\0 & 0 & -1\\1 & 1 & 1\end{bmatrix}\) \(\begin{bmatrix}0 & -1 & 0\\1 & 1 & 1\\-1 & 0 & 0\end{bmatrix}\)\(\begin{bmatrix}-1 & -1 & -1\\0 & 0 & 1\\0 & 1 & 0\end{bmatrix}\) \(\begin{bmatrix}0 & 0 & 1\\-1 & -1 & -1\\1 & 0 & 0\end{bmatrix}\)\(\begin{bmatrix}0 & 1 & 0\\1 & 0 & 0\\-1 & -1 & -1\end{bmatrix}\)
\(\rho_{5,2}\)\(\begin{bmatrix}0 & -1 & 0\\1 & 1 & 1\\-1 & 0 & 0\end{bmatrix}\)\(\begin{bmatrix}0 & -1 & 0\\0 & 0 & -1\\1 & 1 & 1\end{bmatrix}\) \(\begin{bmatrix}0 & 0 & -1\\-1 & 0 & 0\\1 & 1 & 1\end{bmatrix}\)\(\begin{bmatrix}-1 & -1 & -1\\0 & 0 & 1\\0 & 1 & 0\end{bmatrix}\) \(\begin{bmatrix}0 & 0 & 1\\-1 & -1 & -1\\1 & 0 & 0\end{bmatrix}\)\(\begin{bmatrix}0 & 1 & 0\\1 & 0 & 0\\-1 & -1 & -1\end{bmatrix}\)
\(\rho_{5,3}\)\(\begin{bmatrix}1 & 0 & 0\\0 & 0 & -1\\0 & 1 & 0\end{bmatrix}\)\(\begin{bmatrix}0 & 0 & 1\\0 & 1 & 0\\-1 & 0 & 0\end{bmatrix}\) \(\begin{bmatrix}1 & 0 & 0\\0 & 0 & 1\\0 & -1 & 0\end{bmatrix}\)\(\begin{bmatrix}1 & 0 & 0\\0 & -1 & 0\\0 & 0 & -1\end{bmatrix}\) \(\begin{bmatrix}-1 & 0 & 0\\0 & 1 & 0\\0 & 0 & -1\end{bmatrix}\)\(\begin{bmatrix}-1 & 0 & 0\\0 & -1 & 0\\0 & 0 & 1\end{bmatrix}\)



⇦ \(\quad \)
home \(\quad \)
⇨

登録: 投稿 (Atom)