yr205

【第2章】対称群 \(S_4\)

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【2-7】 左正則表現の既約分解結果

【表3】対称群 \(S_4\) の左正則表現を既約分解した小行列
\(S_4\)の巡回表現\( e\)\( (3,4) \)\( (2,3) \)\( (2,4) \)\( (1,2) \)\( (1,3) \)
\(\mathbb{C}[S_4]\)の元\(g_{1}\)\(g_{2}\)\(g_{3}\)\(g_{4}\)\(g_{5}\)\(g_{6}\)
\(row1:\rho_{1}\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(row2,3,4:\rho_{2}\)\(\begin{bmatrix}1 & 0 & 0\\0 & 1 & 0\\0 & 0 & 1\end{bmatrix}\)\(\begin{bmatrix}0 & 1 & 0\\1 & 0 & 0\\0 & 0 & 1\end{bmatrix}\) \(\begin{bmatrix}1 & 0 & 0\\0 & 0 & 1\\0 & 1 & 0\end{bmatrix}\)\(\begin{bmatrix}0 & 0 & 1\\0 & 1 & 0\\1 & 0 & 0\end{bmatrix}\) \(\begin{bmatrix}1 & 0 & -1\\0 & 1 & -1\\0 & 0 & -1\end{bmatrix}\)\(\begin{bmatrix}1 & -1 & 0\\0 & -1 & 0\\0 & -1 & 1\end{bmatrix}\)
\(row5,6,7:\rho_{3}\)\(\begin{bmatrix}1 & 0 & 0\\0 & 1 & 0\\0 & 0 & 1\end{bmatrix}\)\(\begin{bmatrix}0 & 1 & 0\\1 & 0 & 0\\0 & 0 & 1\end{bmatrix}\) \(\begin{bmatrix}0 & 0 & 1\\0 & 1 & 0\\1 & 0 & 0\end{bmatrix}\)\(\begin{bmatrix}1 & 0 & 0\\0 & 0 & 1\\0 & 1 & 0\end{bmatrix}\) \(\begin{bmatrix}1 & 0 & -1\\0 & 1 & -1\\0 & 0 & -1\end{bmatrix}\)\(\begin{bmatrix}-1 & 0 & 0\\-1 & 1 & 0\\-1 & 0 & 1\end{bmatrix}\)
\(row8,9,10:\rho_{4}\) \(\begin{bmatrix}1 & 0 & 0\\0 & 1 & 0\\0 & 0 & 1\end{bmatrix}\)\(\begin{bmatrix}1 & 0 & 0\\0 & 0 & 1\\0 & 1 & 0\end{bmatrix}\) \(\begin{bmatrix}0 & 1 & 0\\1 & 0 & 0\\0 & 0 & 1\end{bmatrix}\)\(\begin{bmatrix}0 & 0 & 1\\0 & 1 & 0\\1 & 0 & 0\end{bmatrix}\) \(\begin{bmatrix}-1 & 0 & 0\\-1 & 1 & 0\\-1 & 0 & 1\end{bmatrix}\)\(\begin{bmatrix}1 & -1 & 0\\0 & -1 & 0\\0 & -1 & 1\end{bmatrix}\)
\(row11,12:\rho_{5}\)\(\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}\)\(\begin{bmatrix}1 & -1\\0 & -1\end{bmatrix}\)\(\begin{bmatrix}0 & 1\\1 & 0\end{bmatrix}\) \(\begin{bmatrix}-1 & 0\\-1 & 1\end{bmatrix}\)\(\begin{bmatrix}1 & -1\\0 & -1\end{bmatrix}\)\(\begin{bmatrix}-1 & 0\\-1 & 1\end{bmatrix}\)
\(row13,14:\rho_{6}\) \(\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}\)\(\begin{bmatrix}0 & 1\\1 & 0\end{bmatrix}\)\(\begin{bmatrix}-1 & 0\\-1 & 1\end{bmatrix}\) \(\begin{bmatrix}1 & -1\\0 & -1\end{bmatrix}\)\(\begin{bmatrix}0 & 1\\1 & 0\end{bmatrix}\)\(\begin{bmatrix}1 & -1\\0 & -1\end{bmatrix}\)
\(row15,16,17:\rho_{7}\)\(\begin{bmatrix}1 & 0 & 0\\0 & 1 & 0\\0 & 0 & 1\end{bmatrix}\)\(\begin{bmatrix}-1 & 0 & 0\\0 & 0 & -1\\0 & -1 & 0\end{bmatrix}\) \(\begin{bmatrix}0 & 1 & 0\\1 & 0 & 0\\0 & 0 & -1\end{bmatrix}\)\(\begin{bmatrix}0 & 0 & 1\\0 & -1 & 0\\1 & 0 & 0\end{bmatrix}\) \(\begin{bmatrix}1 & -1 & -1\\0 & -1 & 0\\0 & 0 & -1\end{bmatrix}\)\(\begin{bmatrix}-1 & 0 & 0\\-1 & 1 & 1\\0 & 0 & -1\end{bmatrix}\)
\(row18,19,20:\rho_{8}\)\(\begin{bmatrix}1 & 0 & 0\\0 & 1 & 0\\0 & 0 & 1\end{bmatrix}\)\(\begin{bmatrix}0 & 1 & 0\\1 & 0 & 0\\0 & 0 & -1\end{bmatrix}\) \(\begin{bmatrix}0 & 0 & 1\\0 & -1 & 0\\1 & 0 & 0\end{bmatrix}\)\(\begin{bmatrix}-1 & 0 & 0\\0 & 0 & -1\\0 & -1 & 0\end{bmatrix}\) \(\begin{bmatrix}-1 & 0 & 0\\0 & -1 & 0\\-1 & 1 & 1\end{bmatrix}\)\(\begin{bmatrix}1 & -1 & -1\\0 & -1 & 0\\0 & 0 & -1\end{bmatrix}\)
\(row21,22,23:\rho_{9}\)\(\begin{bmatrix}1 & 0 & 0\\0 & 1 & 0\\0 & 0 & 1\end{bmatrix}\)\(\begin{bmatrix}0 & 1 & 0\\1 & 0 & 0\\0 & 0 & -1\end{bmatrix}\) \(\begin{bmatrix}-1 & 0 & 0\\0 & 0 & -1\\0 & -1 & 0\end{bmatrix}\)\(\begin{bmatrix}0 & 0 & 1\\0 & -1 & 0\\1 & 0 & 0\end{bmatrix}\) \(\begin{bmatrix}-1 & 0 & 0\\0 & -1 & 0\\-1 & 1 & 1\end{bmatrix}\)\(\begin{bmatrix}-1 & 0 & 0\\-1 & 1 & 1\\0 & 0 & -1\end{bmatrix}\)
\(row24:\rho_{10}\)\(1\)\(-1\)\(-1\)\(-1\)\(-1\)\(-1\)
\(S_4\)の巡回表現\( (1,4) \)\( (2,3,4) \)\( (2,4,3) \)\( (1,2,3) \)\( (1,2,4) \)\( (1,3,2) \)
\(\mathbb{C}[S_4]\)の元\(g_{7}\)\(g_{8}\)\(g_{9}\)\(g_{10}\)\(g_{11}\)\(g_{12}\)
\(row1:\rho_{1}\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(row2,3,4:\rho_{2}\)\(\begin{bmatrix}-1 & 0 & 0\\-1 & 1 & 0\\-1 & 0 & 1\end{bmatrix}\)\(\begin{bmatrix}0 & 1 & 0\\0 & 0 & 1\\1 & 0 & 0\end{bmatrix}\) \(\begin{bmatrix}0 & 0 & 1\\1 & 0 & 0\\0 & 1 & 0\end{bmatrix}\)\(\begin{bmatrix}1 & -1 & 0\\0 & -1 & 1\\0 & -1 & 0\end{bmatrix}\) \(\begin{bmatrix}-1 & 0 & 1\\-1 & 1 & 0\\-1 & 0 & 0\end{bmatrix}\)\(\begin{bmatrix}1 & 0 & -1\\0 & 0 & -1\\0 & 1 & -1\end{bmatrix}\)
\(row5,6,7:\rho_{3}\)\(\begin{bmatrix}1 & -1 & 0\\0 & -1 & 0\\0 & -1 & 1\end{bmatrix}\)\(\begin{bmatrix}0 & 0 & 1\\1 & 0 & 0\\0 & 1 & 0\end{bmatrix}\) \(\begin{bmatrix}0 & 1 & 0\\0 & 0 & 1\\1 & 0 & 0\end{bmatrix}\)\(\begin{bmatrix}-1 & 0 & 1\\-1 & 1 & 0\\-1 & 0 & 0\end{bmatrix}\) \(\begin{bmatrix}1 & -1 & 0\\0 & -1 & 1\\0 & -1 & 0\end{bmatrix}\)\(\begin{bmatrix}0 & 0 & -1\\0 & 1 & -1\\1 & 0 & -1\end{bmatrix}\)
\(row8,9,10:\rho_{4}\) \(\begin{bmatrix}1 & 0 & -1\\0 & 1 & -1\\0 & 0 & -1\end{bmatrix}\)\(\begin{bmatrix}0 & 0 & 1\\1 & 0 & 0\\0 & 1 & 0\end{bmatrix}\) \(\begin{bmatrix}0 & 1 & 0\\0 & 0 & 1\\1 & 0 & 0\end{bmatrix}\)\(\begin{bmatrix}0 & -1 & 0\\1 & -1 & 0\\0 & -1 & 1\end{bmatrix}\) \(\begin{bmatrix}0 & 0 & -1\\0 & 1 & -1\\1 & 0 & -1\end{bmatrix}\)\(\begin{bmatrix}-1 & 1 & 0\\-1 & 0 & 0\\-1 & 0 & 1\end{bmatrix}\)
\(row11,12:\rho_{5}\) \(\begin{bmatrix}0 & 1\\1 & 0\end{bmatrix}\)\(\begin{bmatrix}0 & -1\\1 & -1\end{bmatrix}\)\(\begin{bmatrix}-1 & 1\\-1 & 0\end{bmatrix}\) \(\begin{bmatrix}-1 & 1\\-1 & 0\end{bmatrix}\)\(\begin{bmatrix}0 & -1\\1 & -1\end{bmatrix}\)\(\begin{bmatrix}0 & -1\\1 & -1\end{bmatrix}\)
\(row13,14:\rho_{6}\)\(\begin{bmatrix}-1 & 0\\-1 & 1\end{bmatrix}\)\(\begin{bmatrix}0 & -1\\1 & -1\end{bmatrix}\)\(\begin{bmatrix}-1 & 1\\-1 & 0\end{bmatrix}\) \(\begin{bmatrix}-1 & 1\\-1 & 0\end{bmatrix}\)\(\begin{bmatrix}0 & -1\\1 & -1\end{bmatrix}\)\(\begin{bmatrix}0 & -1\\1 & -1\end{bmatrix}\)
\(row15,16,17:\rho_{7}\)\(\begin{bmatrix}-1 & 0 & 0\\0 & -1 & 0\\-1 & 1 & 1\end{bmatrix}\)\(\begin{bmatrix}0 & 0 & -1\\-1 & 0 & 0\\0 & 1 & 0\end{bmatrix}\) \(\begin{bmatrix}0 & -1 & 0\\0 & 0 & 1\\-1 & 0 & 0\end{bmatrix}\)\(\begin{bmatrix}-1 & 1 & 1\\-1 & 0 & 0\\0 & 0 & 1\end{bmatrix}\) \(\begin{bmatrix}-1 & 1 & 1\\0 & 1 & 0\\-1 & 0 & 0\end{bmatrix}\)\(\begin{bmatrix}0 & -1 & 0\\1 & -1 & -1\\0 & 0 & 1\end{bmatrix}\)
\(row18,19,20:\rho_{8}\)\(\begin{bmatrix}-1 & 0 & 0\\-1 & 1 & 1\\0 & 0 & -1\end{bmatrix}\)\(\begin{bmatrix}0 & 0 & -1\\-1 & 0 & 0\\0 & 1 & 0\end{bmatrix}\) \(\begin{bmatrix}0 & -1 & 0\\0 & 0 & 1\\-1 & 0 & 0\end{bmatrix}\)\(\begin{bmatrix}0 & 0 & -1\\0 & 1 & 0\\1 & -1 & -1\end{bmatrix}\) \(\begin{bmatrix}1 & 0 & 0\\0 & 0 & 1\\1 & -1 & -1\end{bmatrix}\)\(\begin{bmatrix}-1 & 1 & 1\\0 & 1 & 0\\-1 & 0 & 0\end{bmatrix}\)
\(row21,22,23:\rho_{9}\)\(\begin{bmatrix}1 & -1 & -1\\0 & -1 & 0\\0 & 0 & -1\end{bmatrix}\)\(\begin{bmatrix}0 & -1 & 0\\0 & 0 & 1\\-1 & 0 & 0\end{bmatrix}\) \(\begin{bmatrix}0 & 0 & -1\\-1 & 0 & 0\\0 & 1 & 0\end{bmatrix}\)\(\begin{bmatrix}1 & 0 & 0\\0 & 0 & 1\\1 & -1 & -1\end{bmatrix}\) \(\begin{bmatrix}0 & 0 & -1\\0 & 1 & 0\\1 & -1 & -1\end{bmatrix}\)\(\begin{bmatrix}1 & 0 & 0\\1 & -1 & -1\\0 & 1 & 0\end{bmatrix}\)
\(row24:\rho_{10}\)\(-1\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(S_4\)の巡回表現\( (1,3,4) \)\( (1,4,2) \)\( (1,4,3) \)\( (1,2,3,4) \)\( (1,2,4,3) \)\( (1,3,4,2) \)
\(\mathbb{C}[S_4]\)の元\(g_{13}\)\(g_{14}\)\(g_{15}\)\(g_{16}\)\(g_{17}\)\(g_{18}\)
\(row1:\rho_{1}\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(row2,3,4:\rho_{2}\)\(\begin{bmatrix}-1 & 1 & 0\\-1 & 0 & 0\\-1 & 0 & 1\end{bmatrix}\)\(\begin{bmatrix}0 & 0 & -1\\0 & 1 & -1\\1 & 0 & -1\end{bmatrix}\) \(\begin{bmatrix}0 & -1 & 0\\1 & -1 & 0\\0 & -1 & 1\end{bmatrix}\)\(\begin{bmatrix}-1 & 1 & 0\\-1 & 0 & 1\\-1 & 0 & 0\end{bmatrix}\) \(\begin{bmatrix}0 & -1 & 1\\1 & -1 & 0\\0 & -1 & 0\end{bmatrix}\)\(\begin{bmatrix}0 & 1 & -1\\0 & 0 & -1\\1 & 0 & -1\end{bmatrix}\)
\(row5,6,7:\rho_{3}\)\(\begin{bmatrix}0 & -1 & 0\\1 & -1 & 0\\0 & -1 & 1\end{bmatrix}\)\(\begin{bmatrix}1 & 0 & -1\\0 & 0 & -1\\0 & 1 & -1\end{bmatrix}\) \(\begin{bmatrix}-1 & 1 & 0\\-1 & 0 & 0\\-1 & 0 & 1\end{bmatrix}\)\(\begin{bmatrix}0 & -1 & 1\\1 & -1 & 0\\0 & -1 & 0\end{bmatrix}\) \(\begin{bmatrix}-1 & 1 & 0\\-1 & 0 & 1\\-1 & 0 & 0\end{bmatrix}\)\(\begin{bmatrix}0 & 0 & -1\\1 & 0 & -1\\0 & 1 & -1\end{bmatrix}\)
\(row8,9,10:\rho_{4}\)\(\begin{bmatrix}1 & 0 & -1\\0 & 0 & -1\\0 & 1 & -1\end{bmatrix}\)\(\begin{bmatrix}-1 & 0 & 1\\-1 & 1 & 0\\-1 & 0 & 0\end{bmatrix}\) \(\begin{bmatrix}1 & -1 & 0\\0 & -1 & 1\\0 & -1 & 0\end{bmatrix}\)\(\begin{bmatrix}0 & 0 & -1\\1 & 0 & -1\\0 & 1 & -1\end{bmatrix}\) \(\begin{bmatrix}0 & -1 & 0\\0 & -1 & 1\\1 & -1 & 0\end{bmatrix}\)\(\begin{bmatrix}-1 & 0 & 1\\-1 & 0 & 0\\-1 & 1 & 0\end{bmatrix}\)
\(row11,12:\rho_{5}\) \(\begin{bmatrix}-1 & 1\\-1 & 0\end{bmatrix}\)\(\begin{bmatrix}-1 & 1\\-1 & 0\end{bmatrix}\)\(\begin{bmatrix}0 & -1\\1 & -1\end{bmatrix}\) \(\begin{bmatrix}-1 & 0\\-1 & 1\end{bmatrix}\)\(\begin{bmatrix}0 & 1\\1 & 0\end{bmatrix}\)\(\begin{bmatrix}0 & 1\\1 & 0\end{bmatrix}\)
\(row13,14:\rho_{6}\)\(\begin{bmatrix}-1 & 1\\-1 & 0\end{bmatrix}\)\(\begin{bmatrix}-1 & 1\\-1 & 0\end{bmatrix}\)\(\begin{bmatrix}0 & -1\\1 & -1\end{bmatrix}\) \(\begin{bmatrix}1 & -1\\0 & -1\end{bmatrix}\)\(\begin{bmatrix}-1 & 0\\-1 & 1\end{bmatrix}\)\(\begin{bmatrix}-1 & 0\\-1 & 1\end{bmatrix}\)
\(row15,16,17:\rho_{7}\)\(\begin{bmatrix}1 & 0 & 0\\1 & -1 & -1\\0 & 1 & 0\end{bmatrix}\)\(\begin{bmatrix}0 & 0 & -1\\0 & 1 & 0\\1 & -1 & -1\end{bmatrix}\) \(\begin{bmatrix}1 & 0 & 0\\0 & 0 & 1\\1 & -1 & -1\end{bmatrix}\)\(\begin{bmatrix}1 & -1 & -1\\1 & 0 & 0\\0 & -1 & 0\end{bmatrix}\) \(\begin{bmatrix}1 & -1 & -1\\0 & 0 & -1\\1 & 0 & 0\end{bmatrix}\)\(\begin{bmatrix}0 & 0 & 1\\-1 & 1 & 1\\0 & -1 & 0\end{bmatrix}\)
\(row18,19,20:\rho_{8}\)\(\begin{bmatrix}-1 & 1 & 1\\-1 & 0 & 0\\0 & 0 & 1\end{bmatrix}\)\(\begin{bmatrix}1 & 0 & 0\\1 & -1 & -1\\0 & 1 & 0\end{bmatrix}\) \(\begin{bmatrix}0 & -1 & 0\\1 & -1 & -1\\0 & 0 & 1\end{bmatrix}\)\(\begin{bmatrix}0 & 0 & 1\\1 & 0 & 0\\-1 & 1 & 1\end{bmatrix}\) \(\begin{bmatrix}0 & 1 & 0\\0 & 0 & -1\\-1 & 1 & 1\end{bmatrix}\)\(\begin{bmatrix}1 & -1 & -1\\1 & 0 & 0\\0 & -1 & 0\end{bmatrix}\)
\(row21,22,23:\rho_{9}\)\(\begin{bmatrix}0 & -1 & 0\\1 & -1 & -1\\0 & 0 & 1\end{bmatrix}\)\(\begin{bmatrix}-1 & 1 & 1\\0 & 1 & 0\\-1 & 0 & 0\end{bmatrix}\) \(\begin{bmatrix}-1 & 1 & 1\\-1 & 0 & 0\\0 & 0 & 1\end{bmatrix}\)\(\begin{bmatrix}0 & 1 & 0\\0 & 0 & -1\\-1 & 1 & 1\end{bmatrix}\) \(\begin{bmatrix}0 & 0 & 1\\1 & 0 & 0\\-1 & 1 & 1\end{bmatrix}\)\(\begin{bmatrix}0 & 1 & 0\\-1 & 1 & 1\\1 & 0 & 0\end{bmatrix}\)
\(row24:\rho_{10}\)\(1\)\(1\)\(1\)\(-1\)\(-1\)\(-1\)
\(S_4\)の巡回表現\( (1,3,2,4) \)\( (1,4,3,2) \)\( (1,4,2,3) \)\( (1,2)(3,4) \)\( (1,3)(2,4) \)\( (1,4)(2,3) \)
\(\mathbb{C}[S_4]\)の元\(g_{19}\)\(g_{20}\)\(g_{21}\)\(g_{22}\)\(g_{23}\)\(g_{24}\)
\(row1:\rho_{1}\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(row2,3,4:\rho_{2}\)\(\begin{bmatrix}-1 & 0 & 1\\-1 & 0 & 0\\-1 & 1 & 0\end{bmatrix}\)\(\begin{bmatrix}0 & 0 & -1\\1 & 0 & -1\\0 & 1 & -1\end{bmatrix}\) \(\begin{bmatrix}0 & -1 & 0\\0 & -1 & 1\\1 & -1 & 0\end{bmatrix}\)\(\begin{bmatrix}0 & 1 & -1\\1 & 0 & -1\\0 & 0 & -1\end{bmatrix}\) \(\begin{bmatrix}0 & -1 & 1\\0 & -1 & 0\\1 & -1 & 0\end{bmatrix}\)\(\begin{bmatrix}-1 & 0 & 0\\-1 & 0 & 1\\-1 & 1 & 0\end{bmatrix}\)
\(row5,6,7:\rho_{3}\)\(\begin{bmatrix}0 & -1 & 0\\0 & -1 & 1\\1 & -1 & 0\end{bmatrix}\)\(\begin{bmatrix}0 & 1 & -1\\0 & 0 & -1\\1 & 0 & -1\end{bmatrix}\) \(\begin{bmatrix}-1 & 0 & 1\\-1 & 0 & 0\\-1 & 1 & 0\end{bmatrix}\)\(\begin{bmatrix}0 & 1 & -1\\1 & 0 & -1\\0 & 0 & -1\end{bmatrix}\) \(\begin{bmatrix}-1 & 0 & 0\\-1 & 0 & 1\\-1 & 1 & 0\end{bmatrix}\)\(\begin{bmatrix}0 & -1 & 1\\0 & -1 & 0\\1 & -1 & 0\end{bmatrix}\)
\(row8,9,10:\rho_{4}\)\(\begin{bmatrix}0 & 1 & -1\\0 & 0 & -1\\1 & 0 & -1\end{bmatrix}\)\(\begin{bmatrix}-1 & 1 & 0\\-1 & 0 & 1\\-1 & 0 & 0\end{bmatrix}\) \(\begin{bmatrix}0 & -1 & 1\\1 & -1 & 0\\0 & -1 & 0\end{bmatrix}\)\(\begin{bmatrix}-1 & 0 & 0\\-1 & 0 & 1\\-1 & 1 & 0\end{bmatrix}\) \(\begin{bmatrix}0 & -1 & 1\\0 & -1 & 0\\1 & -1 & 0\end{bmatrix}\)\(\begin{bmatrix}0 & 1 & -1\\1 & 0 & -1\\0 & 0 & -1\end{bmatrix}\)
\(row11,12:\rho_{5}\)\(\begin{bmatrix}1 & -1\\0 & -1\end{bmatrix}\)\(\begin{bmatrix}-1 & 0\\-1 & 1\end{bmatrix}\)\(\begin{bmatrix}1 & -1\\0 & -1\end{bmatrix}\) \(\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}\)\(\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}\)\(\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}\)
\(row13,14:\rho_{6}\)\(\begin{bmatrix}0 & 1\\1 & 0\end{bmatrix}\)\(\begin{bmatrix}1 & -1\\0 & -1\end{bmatrix}\)\(\begin{bmatrix}0 & 1\\1 & 0\end{bmatrix}\) \(\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}\)\(\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}\)\(\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}\)
\(row15,16,17:\rho_{7}\)\(\begin{bmatrix}0 & 1 & 0\\-1 & 1 & 1\\1 & 0 & 0\end{bmatrix}\)\(\begin{bmatrix}0 & 1 & 0\\0 & 0 & -1\\-1 & 1 & 1\end{bmatrix}\) \(\begin{bmatrix}0 & 0 & 1\\1 & 0 & 0\\-1 & 1 & 1\end{bmatrix}\)\(\begin{bmatrix}-1 & 1 & 1\\0 & 0 & 1\\0 & 1 & 0\end{bmatrix}\) \(\begin{bmatrix}0 & 0 & -1\\1 & -1 & -1\\-1 & 0 & 0\end{bmatrix}\)\(\begin{bmatrix}0 & -1 & 0\\-1 & 0 & 0\\1 & -1 & -1\end{bmatrix}\)
\(row18,19,20:\rho_{8}\)\(\begin{bmatrix}1 & -1 & -1\\0 & 0 & -1\\1 & 0 & 0\end{bmatrix}\)\(\begin{bmatrix}0 & 1 & 0\\-1 & 1 & 1\\1 & 0 & 0\end{bmatrix}\) \(\begin{bmatrix}0 & 0 & 1\\-1 & 1 & 1\\0 & -1 & 0\end{bmatrix}\)\(\begin{bmatrix}0 & -1 & 0\\-1 & 0 & 0\\1 & -1 & -1\end{bmatrix}\) \(\begin{bmatrix}-1 & 1 & 1\\0 & 0 & 1\\0 & 1 & 0\end{bmatrix}\)\(\begin{bmatrix}0 & 0 & -1\\1 & -1 & -1\\-1 & 0 & 0\end{bmatrix}\)
\(row21,22,23:\rho_{9}\)\(\begin{bmatrix}0 & 0 & 1\\-1 & 1 & 1\\0 & -1 & 0\end{bmatrix}\)\(\begin{bmatrix}1 & -1 & -1\\1 & 0 & 0\\0 & -1 & 0\end{bmatrix}\) \(\begin{bmatrix}1 & -1 & -1\\0 & 0 & -1\\1 & 0 & 0\end{bmatrix}\)\(\begin{bmatrix}0 & -1 & 0\\-1 & 0 & 0\\1 & -1 & -1\end{bmatrix}\) \(\begin{bmatrix}0 & 0 & -1\\1 & -1 & -1\\-1 & 0 & 0\end{bmatrix}\)\(\begin{bmatrix}-1 & 1 & 1\\0 & 0 & 1\\0 & 1 & 0\end{bmatrix}\)
\(row24:\rho_{10}\)\(-1\)\(-1\)\(-1\)\(1\)\(1\)\(1\)



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home \(\quad \)
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