SO(14) 2 | VerlindeDB

\(\operatorname{SO}(14)_{2}\): \( D_{7} \) at level \(2\)

Fusion Ring

\[ \begin{array}{llllllllllllll} \htmlTitle{1\otimes 1}{1} & & & & & & & & & & & & & \\ \htmlTitle{2\otimes 1}{2} & \htmlTitle{2\otimes 2}{1} & & & & & & & & & & & & \\ \htmlTitle{3\otimes 1}{3} & \htmlTitle{3\otimes 2}{4} & \htmlTitle{3\otimes 3}{2} & & & & & & & & & & & \\ \htmlTitle{4\otimes 1}{4} & \htmlTitle{4\otimes 2}{3} & \htmlTitle{4\otimes 3}{1} & \htmlTitle{4\otimes 4}{2} & & & & & & & & & & \\ \htmlTitle{5\otimes 1}{5} & \htmlTitle{5\otimes 2}{5} & \htmlTitle{5\otimes 3}{10} & \htmlTitle{5\otimes 4}{10} & \htmlTitle{5\otimes 5}{1 \oplus 6 \oplus 2} & & & & & & & & & \\ \htmlTitle{6\otimes 1}{6} & \htmlTitle{6\otimes 2}{6} & \htmlTitle{6\otimes 3}{9} & \htmlTitle{6\otimes 4}{9} & \htmlTitle{6\otimes 5}{5 \oplus 7} & \htmlTitle{6\otimes 6}{1 \oplus 8 \oplus 2} & & & & & & & & \\ \htmlTitle{7\otimes 1}{7} & \htmlTitle{7\otimes 2}{7} & \htmlTitle{7\otimes 3}{8} & \htmlTitle{7\otimes 4}{8} & \htmlTitle{7\otimes 5}{6 \oplus 8} & \htmlTitle{7\otimes 6}{5 \oplus 9} & \htmlTitle{7\otimes 7}{1 \oplus 10 \oplus 2} & & & & & & & \\ \htmlTitle{8\otimes 1}{8} & \htmlTitle{8\otimes 2}{8} & \htmlTitle{8\otimes 3}{7} & \htmlTitle{8\otimes 4}{7} & \htmlTitle{8\otimes 5}{7 \oplus 9} & \htmlTitle{8\otimes 6}{6 \oplus 10} & \htmlTitle{8\otimes 7}{5 \oplus 3 \oplus 4} & \htmlTitle{8\otimes 8}{1 \oplus 10 \oplus 2} & & & & & & \\ \htmlTitle{9\otimes 1}{9} & \htmlTitle{9\otimes 2}{9} & \htmlTitle{9\otimes 3}{6} & \htmlTitle{9\otimes 4}{6} & \htmlTitle{9\otimes 5}{8 \oplus 10} & \htmlTitle{9\otimes 6}{7 \oplus 3 \oplus 4} & \htmlTitle{9\otimes 7}{6 \oplus 10} & \htmlTitle{9\otimes 8}{5 \oplus 9} & \htmlTitle{9\otimes 9}{1 \oplus 8 \oplus 2} & & & & & \\ \htmlTitle{10\otimes 1}{10} & \htmlTitle{10\otimes 2}{10} & \htmlTitle{10\otimes 3}{5} & \htmlTitle{10\otimes 4}{5} & \htmlTitle{10\otimes 5}{9 \oplus 3 \oplus 4} & \htmlTitle{10\otimes 6}{8 \oplus 10} & \htmlTitle{10\otimes 7}{7 \oplus 9} & \htmlTitle{10\otimes 8}{6 \oplus 8} & \htmlTitle{10\otimes 9}{5 \oplus 7} & \htmlTitle{10\otimes 10}{1 \oplus 6 \oplus 2} & & & & \\ \htmlTitle{11\otimes 1}{11} & \htmlTitle{11\otimes 2}{14} & \htmlTitle{11\otimes 3}{13} & \htmlTitle{11\otimes 4}{12} & \htmlTitle{11\otimes 5}{12 \oplus 13} & \htmlTitle{11\otimes 6}{11 \oplus 14} & \htmlTitle{11\otimes 7}{12 \oplus 13} & \htmlTitle{11\otimes 8}{11 \oplus 14} & \htmlTitle{11\otimes 9}{12 \oplus 13} & \htmlTitle{11\otimes 10}{11 \oplus 14} & \htmlTitle{11\otimes 11}{5 \oplus 7 \oplus 9 \oplus 3} & & & \\ \htmlTitle{12\otimes 1}{12} & \htmlTitle{12\otimes 2}{13} & \htmlTitle{12\otimes 3}{11} & \htmlTitle{12\otimes 4}{14} & \htmlTitle{12\otimes 5}{11 \oplus 14} & \htmlTitle{12\otimes 6}{12 \oplus 13} & \htmlTitle{12\otimes 7}{11 \oplus 14} & \htmlTitle{12\otimes 8}{12 \oplus 13} & \htmlTitle{12\otimes 9}{11 \oplus 14} & \htmlTitle{12\otimes 10}{12 \oplus 13} & \htmlTitle{12\otimes 11}{1 \oplus 6 \oplus 8 \oplus 10} & \htmlTitle{12\otimes 12}{5 \oplus 7 \oplus 9 \oplus 4} & & \\ \htmlTitle{13\otimes 1}{13} & \htmlTitle{13\otimes 2}{12} & \htmlTitle{13\otimes 3}{14} & \htmlTitle{13\otimes 4}{11} & \htmlTitle{13\otimes 5}{11 \oplus 14} & \htmlTitle{13\otimes 6}{12 \oplus 13} & \htmlTitle{13\otimes 7}{11 \oplus 14} & \htmlTitle{13\otimes 8}{12 \oplus 13} & \htmlTitle{13\otimes 9}{11 \oplus 14} & \htmlTitle{13\otimes 10}{12 \oplus 13} & \htmlTitle{13\otimes 11}{6 \oplus 8 \oplus 10 \oplus 2} & \htmlTitle{13\otimes 12}{5 \oplus 7 \oplus 9 \oplus 3} & \htmlTitle{13\otimes 13}{5 \oplus 7 \oplus 9 \oplus 4} & \\ \htmlTitle{14\otimes 1}{14} & \htmlTitle{14\otimes 2}{11} & \htmlTitle{14\otimes 3}{12} & \htmlTitle{14\otimes 4}{13} & \htmlTitle{14\otimes 5}{12 \oplus 13} & \htmlTitle{14\otimes 6}{11 \oplus 14} & \htmlTitle{14\otimes 7}{12 \oplus 13} & \htmlTitle{14\otimes 8}{11 \oplus 14} & \htmlTitle{14\otimes 9}{12 \oplus 13} & \htmlTitle{14\otimes 10}{11 \oplus 14} & \htmlTitle{14\otimes 11}{5 \oplus 7 \oplus 9 \oplus 4} & \htmlTitle{14\otimes 12}{6 \oplus 8 \oplus 10 \oplus 2} & \htmlTitle{14\otimes 13}{1 \oplus 6 \oplus 8 \oplus 10} & \htmlTitle{14\otimes 14}{5 \oplus 7 \oplus 9 \oplus 3} \\ \end{array} \]

Frobenius-Perron Dimensions

SimpleNumericSymbolic
\( 1\)\(1.000\)\( 1 \)
\( 2\)\(1.000\)\( 1 \)
\( 3\)\(1.000\)\( 1 \)
\( 4\)\(1.000\)\( 1 \)
\( 5\)\(2.000\)\( 2 \)
\( 6\)\(2.000\)\( 2 \)
\( 7\)\(2.000\)\( 2 \)
\( 8\)\(2.000\)\( 2 \)
\( 9\)\(2.000\)\( 2 \)
\( 10\)\(2.000\)\( 2 \)
\( 11\)\(2.646\)\( - 2 \cos{\left(\frac{5 \pi}{14} \right)} + 2 \cos{\left(\frac{3 \pi}{14} \right)} + 2 \cos{\left(\frac{\pi}{14} \right)} \)
\( 12\)\(2.646\)\( - 2 \cos{\left(\frac{5 \pi}{14} \right)} + 2 \cos{\left(\frac{3 \pi}{14} \right)} + 2 \cos{\left(\frac{\pi}{14} \right)} \)
\( 13\)\(2.646\)\( - 2 \cos{\left(\frac{5 \pi}{14} \right)} + 2 \cos{\left(\frac{3 \pi}{14} \right)} + 2 \cos{\left(\frac{\pi}{14} \right)} \)
\( 14\)\(2.646\)\( - 2 \cos{\left(\frac{5 \pi}{14} \right)} + 2 \cos{\left(\frac{3 \pi}{14} \right)} + 2 \cos{\left(\frac{\pi}{14} \right)} \)
\( D^2\)56.000\(56\)

Modular Data

Twist Factors

\[ \begin{pmatrix} \htmlTitle{\theta_{1}}{0} & \htmlTitle{\theta_{2}}{0} & \htmlTitle{\theta_{3}}{\frac{3}{2}} & \htmlTitle{\theta_{4}}{\frac{3}{2}} & \htmlTitle{\theta_{5}}{\frac{13}{14}} & \htmlTitle{\theta_{6}}{\frac{12}{7}} & \htmlTitle{\theta_{7}}{\frac{5}{14}} & \htmlTitle{\theta_{8}}{\frac{6}{7}} & \htmlTitle{\theta_{9}}{\frac{17}{14}} & \htmlTitle{\theta_{10}}{\frac{10}{7}} & \htmlTitle{\theta_{11}}{\frac{13}{8}} & \htmlTitle{\theta_{12}}{\frac{13}{8}} & \htmlTitle{\theta_{13}}{\frac{5}{8}} & \htmlTitle{\theta_{14}}{\frac{5}{8}} \end{pmatrix} \]

S Matrix

\[ \left(\begin{array}{llllllllllllll} \htmlTitle{S_{1; 1}}{1} & & & & & & & & & & & & & \\ \htmlTitle{S_{2; 1}}{1} & \htmlTitle{S_{2; 2}}{1} & & & & & & & & & & & & \\ \htmlTitle{S_{3; 1}}{1} & \htmlTitle{S_{3; 2}}{1} & \htmlTitle{S_{3; 3}}{-1} & & & & & & & & & & & \\ \htmlTitle{S_{4; 1}}{1} & \htmlTitle{S_{4; 2}}{1} & \htmlTitle{S_{4; 3}}{-1} & \htmlTitle{S_{4; 4}}{-1} & & & & & & & & & & \\ \htmlTitle{S_{5; 1}}{2} & \htmlTitle{S_{5; 2}}{2} & \htmlTitle{S_{5; 3}}{-2} & \htmlTitle{S_{5; 4}}{-2} & \htmlTitle{S_{5; 5}}{-2 \zeta_{112}^{40} + 2 \zeta_{112}^{32} - 2 \zeta_{112}^{24} + 2 \zeta_{112}^{16} + 2} & & & & & & & & & \\ \htmlTitle{S_{6; 1}}{2} & \htmlTitle{S_{6; 2}}{2} & \htmlTitle{S_{6; 3}}{2} & \htmlTitle{S_{6; 4}}{2} & \htmlTitle{S_{6; 5}}{-2 \zeta_{112}^{40} + 2 \zeta_{112}^{16}} & \htmlTitle{S_{6; 6}}{2 \zeta_{112}^{32} - 2 \zeta_{112}^{24}} & & & & & & & & \\ \htmlTitle{S_{7; 1}}{2} & \htmlTitle{S_{7; 2}}{2} & \htmlTitle{S_{7; 3}}{-2} & \htmlTitle{S_{7; 4}}{-2} & \htmlTitle{S_{7; 5}}{-2 \zeta_{112}^{32} + 2 \zeta_{112}^{24}} & \htmlTitle{S_{7; 6}}{2 \zeta_{112}^{40} - 2 \zeta_{112}^{32} + 2 \zeta_{112}^{24} - 2 \zeta_{112}^{16} - 2} & \htmlTitle{S_{7; 7}}{2 \zeta_{112}^{40} - 2 \zeta_{112}^{16}} & & & & & & & \\ \htmlTitle{S_{8; 1}}{2} & \htmlTitle{S_{8; 2}}{2} & \htmlTitle{S_{8; 3}}{2} & \htmlTitle{S_{8; 4}}{2} & \htmlTitle{S_{8; 5}}{2 \zeta_{112}^{32} - 2 \zeta_{112}^{24}} & \htmlTitle{S_{8; 6}}{2 \zeta_{112}^{40} - 2 \zeta_{112}^{32} + 2 \zeta_{112}^{24} - 2 \zeta_{112}^{16} - 2} & \htmlTitle{S_{8; 7}}{-2 \zeta_{112}^{40} + 2 \zeta_{112}^{16}} & \htmlTitle{S_{8; 8}}{-2 \zeta_{112}^{40} + 2 \zeta_{112}^{16}} & & & & & & \\ \htmlTitle{S_{9; 1}}{2} & \htmlTitle{S_{9; 2}}{2} & \htmlTitle{S_{9; 3}}{-2} & \htmlTitle{S_{9; 4}}{-2} & \htmlTitle{S_{9; 5}}{2 \zeta_{112}^{40} - 2 \zeta_{112}^{16}} & \htmlTitle{S_{9; 6}}{2 \zeta_{112}^{32} - 2 \zeta_{112}^{24}} & \htmlTitle{S_{9; 7}}{-2 \zeta_{112}^{40} + 2 \zeta_{112}^{32} - 2 \zeta_{112}^{24} + 2 \zeta_{112}^{16} + 2} & \htmlTitle{S_{9; 8}}{2 \zeta_{112}^{40} - 2 \zeta_{112}^{32} + 2 \zeta_{112}^{24} - 2 \zeta_{112}^{16} - 2} & \htmlTitle{S_{9; 9}}{-2 \zeta_{112}^{32} + 2 \zeta_{112}^{24}} & & & & & \\ \htmlTitle{S_{10; 1}}{2} & \htmlTitle{S_{10; 2}}{2} & \htmlTitle{S_{10; 3}}{2} & \htmlTitle{S_{10; 4}}{2} & \htmlTitle{S_{10; 5}}{2 \zeta_{112}^{40} - 2 \zeta_{112}^{32} + 2 \zeta_{112}^{24} - 2 \zeta_{112}^{16} - 2} & \htmlTitle{S_{10; 6}}{-2 \zeta_{112}^{40} + 2 \zeta_{112}^{16}} & \htmlTitle{S_{10; 7}}{2 \zeta_{112}^{32} - 2 \zeta_{112}^{24}} & \htmlTitle{S_{10; 8}}{2 \zeta_{112}^{32} - 2 \zeta_{112}^{24}} & \htmlTitle{S_{10; 9}}{-2 \zeta_{112}^{40} + 2 \zeta_{112}^{16}} & \htmlTitle{S_{10; 10}}{2 \zeta_{112}^{40} - 2 \zeta_{112}^{32} + 2 \zeta_{112}^{24} - 2 \zeta_{112}^{16} - 2} & & & & \\ \htmlTitle{S_{11; 1}}{-2 \zeta_{112}^{44} + 2 \zeta_{112}^{36} - \zeta_{112}^{28} + 2 \zeta_{112}^{4}} & \htmlTitle{S_{11; 2}}{2 \zeta_{112}^{44} - 2 \zeta_{112}^{36} + \zeta_{112}^{28} - 2 \zeta_{112}^{4}} & \htmlTitle{S_{11; 3}}{2 \zeta_{112}^{32} + 2 \zeta_{112}^{16} - 2 \zeta_{112}^{8} + 1} & \htmlTitle{S_{11; 4}}{-2 \zeta_{112}^{32} - 2 \zeta_{112}^{16} + 2 \zeta_{112}^{8} - 1} & \htmlTitle{S_{11; 5}}{0} & \htmlTitle{S_{11; 6}}{0} & \htmlTitle{S_{11; 7}}{0} & \htmlTitle{S_{11; 8}}{0} & \htmlTitle{S_{11; 9}}{0} & \htmlTitle{S_{11; 10}}{0} & \htmlTitle{S_{11; 11}}{\zeta_{112}^{42} - 2 \zeta_{112}^{34} + 2 \zeta_{112}^{26} + 2 \zeta_{112}^{10}} & & & \\ \htmlTitle{S_{12; 1}}{-2 \zeta_{112}^{44} + 2 \zeta_{112}^{36} - \zeta_{112}^{28} + 2 \zeta_{112}^{4}} & \htmlTitle{S_{12; 2}}{2 \zeta_{112}^{44} - 2 \zeta_{112}^{36} + \zeta_{112}^{28} - 2 \zeta_{112}^{4}} & \htmlTitle{S_{12; 3}}{-2 \zeta_{112}^{32} - 2 \zeta_{112}^{16} + 2 \zeta_{112}^{8} - 1} & \htmlTitle{S_{12; 4}}{2 \zeta_{112}^{32} + 2 \zeta_{112}^{16} - 2 \zeta_{112}^{8} + 1} & \htmlTitle{S_{12; 5}}{0} & \htmlTitle{S_{12; 6}}{0} & \htmlTitle{S_{12; 7}}{0} & \htmlTitle{S_{12; 8}}{0} & \htmlTitle{S_{12; 9}}{0} & \htmlTitle{S_{12; 10}}{0} & \htmlTitle{S_{12; 11}}{-2 \zeta_{112}^{46} - 2 \zeta_{112}^{30} + 2 \zeta_{112}^{22} - \zeta_{112}^{14}} & \htmlTitle{S_{12; 12}}{\zeta_{112}^{42} - 2 \zeta_{112}^{34} + 2 \zeta_{112}^{26} + 2 \zeta_{112}^{10}} & & \\ \htmlTitle{S_{13; 1}}{-2 \zeta_{112}^{44} + 2 \zeta_{112}^{36} - \zeta_{112}^{28} + 2 \zeta_{112}^{4}} & \htmlTitle{S_{13; 2}}{2 \zeta_{112}^{44} - 2 \zeta_{112}^{36} + \zeta_{112}^{28} - 2 \zeta_{112}^{4}} & \htmlTitle{S_{13; 3}}{-2 \zeta_{112}^{32} - 2 \zeta_{112}^{16} + 2 \zeta_{112}^{8} - 1} & \htmlTitle{S_{13; 4}}{2 \zeta_{112}^{32} + 2 \zeta_{112}^{16} - 2 \zeta_{112}^{8} + 1} & \htmlTitle{S_{13; 5}}{0} & \htmlTitle{S_{13; 6}}{0} & \htmlTitle{S_{13; 7}}{0} & \htmlTitle{S_{13; 8}}{0} & \htmlTitle{S_{13; 9}}{0} & \htmlTitle{S_{13; 10}}{0} & \htmlTitle{S_{13; 11}}{2 \zeta_{112}^{46} + 2 \zeta_{112}^{30} - 2 \zeta_{112}^{22} + \zeta_{112}^{14}} & \htmlTitle{S_{13; 12}}{-\zeta_{112}^{42} + 2 \zeta_{112}^{34} - 2 \zeta_{112}^{26} - 2 \zeta_{112}^{10}} & \htmlTitle{S_{13; 13}}{\zeta_{112}^{42} - 2 \zeta_{112}^{34} + 2 \zeta_{112}^{26} + 2 \zeta_{112}^{10}} & \\ \htmlTitle{S_{14; 1}}{-2 \zeta_{112}^{44} + 2 \zeta_{112}^{36} - \zeta_{112}^{28} + 2 \zeta_{112}^{4}} & \htmlTitle{S_{14; 2}}{2 \zeta_{112}^{44} - 2 \zeta_{112}^{36} + \zeta_{112}^{28} - 2 \zeta_{112}^{4}} & \htmlTitle{S_{14; 3}}{2 \zeta_{112}^{32} + 2 \zeta_{112}^{16} - 2 \zeta_{112}^{8} + 1} & \htmlTitle{S_{14; 4}}{-2 \zeta_{112}^{32} - 2 \zeta_{112}^{16} + 2 \zeta_{112}^{8} - 1} & \htmlTitle{S_{14; 5}}{0} & \htmlTitle{S_{14; 6}}{0} & \htmlTitle{S_{14; 7}}{0} & \htmlTitle{S_{14; 8}}{0} & \htmlTitle{S_{14; 9}}{0} & \htmlTitle{S_{14; 10}}{0} & \htmlTitle{S_{14; 11}}{-\zeta_{112}^{42} + 2 \zeta_{112}^{34} - 2 \zeta_{112}^{26} - 2 \zeta_{112}^{10}} & \htmlTitle{S_{14; 12}}{2 \zeta_{112}^{46} + 2 \zeta_{112}^{30} - 2 \zeta_{112}^{22} + \zeta_{112}^{14}} & \htmlTitle{S_{14; 13}}{-2 \zeta_{112}^{46} - 2 \zeta_{112}^{30} + 2 \zeta_{112}^{22} - \zeta_{112}^{14}} & \htmlTitle{S_{14; 14}}{\zeta_{112}^{42} - 2 \zeta_{112}^{34} + 2 \zeta_{112}^{26} + 2 \zeta_{112}^{10}}\end{array}\right) \]

Central Charge

\[c = 13 \]