SO(7) 2 | VerlindeDB

\(\operatorname{SO}(7)_{2}\): \( B_{3} \) at level \(2\)

Fusion Ring

\[ \begin{array}{lllllll} \htmlTitle{1\otimes 1}{1} & & & & & & \\ \htmlTitle{2\otimes 1}{2} & \htmlTitle{2\otimes 2}{1} & & & & & \\ \htmlTitle{3\otimes 1}{3} & \htmlTitle{3\otimes 2}{3} & \htmlTitle{3\otimes 3}{1 \oplus 4 \oplus 2} & & & & \\ \htmlTitle{4\otimes 1}{4} & \htmlTitle{4\otimes 2}{4} & \htmlTitle{4\otimes 3}{3 \oplus 5} & \htmlTitle{4\otimes 4}{1 \oplus 5 \oplus 2} & & & \\ \htmlTitle{5\otimes 1}{5} & \htmlTitle{5\otimes 2}{5} & \htmlTitle{5\otimes 3}{4 \oplus 5} & \htmlTitle{5\otimes 4}{3 \oplus 4} & \htmlTitle{5\otimes 5}{1 \oplus 3 \oplus 2} & & \\ \htmlTitle{6\otimes 1}{6} & \htmlTitle{6\otimes 2}{7} & \htmlTitle{6\otimes 3}{6 \oplus 7} & \htmlTitle{6\otimes 4}{6 \oplus 7} & \htmlTitle{6\otimes 5}{6 \oplus 7} & \htmlTitle{6\otimes 6}{1 \oplus 3 \oplus 4 \oplus 5} & \\ \htmlTitle{7\otimes 1}{7} & \htmlTitle{7\otimes 2}{6} & \htmlTitle{7\otimes 3}{6 \oplus 7} & \htmlTitle{7\otimes 4}{6 \oplus 7} & \htmlTitle{7\otimes 5}{6 \oplus 7} & \htmlTitle{7\otimes 6}{3 \oplus 4 \oplus 5 \oplus 2} & \htmlTitle{7\otimes 7}{1 \oplus 3 \oplus 4 \oplus 5} \\ \end{array} \]

Frobenius-Perron Dimensions

SimpleNumericSymbolic
\( 1\)\(1.000\)\( 1 \)
\( 2\)\(1.000\)\( 1 \)
\( 3\)\(2.000\)\( 2 \)
\( 4\)\(2.000\)\( 2 \)
\( 5\)\(2.000\)\( 2 \)
\( 6\)\(2.646\)\( - 2 \cos{\left(\frac{5 \pi}{14} \right)} + 2 \cos{\left(\frac{3 \pi}{14} \right)} + 2 \cos{\left(\frac{\pi}{14} \right)} \)
\( 7\)\(2.646\)\( - 2 \cos{\left(\frac{5 \pi}{14} \right)} + 2 \cos{\left(\frac{3 \pi}{14} \right)} + 2 \cos{\left(\frac{\pi}{14} \right)} \)
\( D^2\)28.000\(28\)

Modular Data

Twist Factors

\[ \begin{pmatrix} \htmlTitle{\theta_{1}}{0} & \htmlTitle{\theta_{2}}{0} & \htmlTitle{\theta_{3}}{\frac{6}{7}} & \htmlTitle{\theta_{4}}{\frac{10}{7}} & \htmlTitle{\theta_{5}}{\frac{12}{7}} & \htmlTitle{\theta_{6}}{\frac{3}{4}} & \htmlTitle{\theta_{7}}{\frac{7}{4}} \end{pmatrix} \]

S Matrix

\[ \left(\begin{array}{lllllll} \htmlTitle{S_{1; 1}}{1} & & & & & & \\ \htmlTitle{S_{2; 1}}{1} & \htmlTitle{S_{2; 2}}{1} & & & & & \\ \htmlTitle{S_{3; 1}}{2} & \htmlTitle{S_{3; 2}}{2} & \htmlTitle{S_{3; 3}}{-2 \zeta_{56}^{20} + 2 \zeta_{56}^{8}} & & & & \\ \htmlTitle{S_{4; 1}}{2} & \htmlTitle{S_{4; 2}}{2} & \htmlTitle{S_{4; 3}}{2 \zeta_{56}^{16} - 2 \zeta_{56}^{12}} & \htmlTitle{S_{4; 4}}{2 \zeta_{56}^{20} - 2 \zeta_{56}^{16} + 2 \zeta_{56}^{12} - 2 \zeta_{56}^{8} - 2} & & & \\ \htmlTitle{S_{5; 1}}{2} & \htmlTitle{S_{5; 2}}{2} & \htmlTitle{S_{5; 3}}{2 \zeta_{56}^{20} - 2 \zeta_{56}^{16} + 2 \zeta_{56}^{12} - 2 \zeta_{56}^{8} - 2} & \htmlTitle{S_{5; 4}}{-2 \zeta_{56}^{20} + 2 \zeta_{56}^{8}} & \htmlTitle{S_{5; 5}}{2 \zeta_{56}^{16} - 2 \zeta_{56}^{12}} & & \\ \htmlTitle{S_{6; 1}}{-2 \zeta_{56}^{22} + 2 \zeta_{56}^{18} - \zeta_{56}^{14} + 2 \zeta_{56}^{2}} & \htmlTitle{S_{6; 2}}{2 \zeta_{56}^{22} - 2 \zeta_{56}^{18} + \zeta_{56}^{14} - 2 \zeta_{56}^{2}} & \htmlTitle{S_{6; 3}}{0} & \htmlTitle{S_{6; 4}}{0} & \htmlTitle{S_{6; 5}}{0} & \htmlTitle{S_{6; 6}}{-2 \zeta_{56}^{22} + 2 \zeta_{56}^{18} - \zeta_{56}^{14} + 2 \zeta_{56}^{2}} & \\ \htmlTitle{S_{7; 1}}{-2 \zeta_{56}^{22} + 2 \zeta_{56}^{18} - \zeta_{56}^{14} + 2 \zeta_{56}^{2}} & \htmlTitle{S_{7; 2}}{2 \zeta_{56}^{22} - 2 \zeta_{56}^{18} + \zeta_{56}^{14} - 2 \zeta_{56}^{2}} & \htmlTitle{S_{7; 3}}{0} & \htmlTitle{S_{7; 4}}{0} & \htmlTitle{S_{7; 5}}{0} & \htmlTitle{S_{7; 6}}{2 \zeta_{56}^{22} - 2 \zeta_{56}^{18} + \zeta_{56}^{14} - 2 \zeta_{56}^{2}} & \htmlTitle{S_{7; 7}}{-2 \zeta_{56}^{22} + 2 \zeta_{56}^{18} - \zeta_{56}^{14} + 2 \zeta_{56}^{2}}\end{array}\right) \]

Central Charge

\[c = 6 \]