SO(15) 2 | VerlindeDB

\(\operatorname{SO}(15)_{2}\): \( B_{7} \) at level \(2\)

Fusion Ring

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

Frobenius-Perron Dimensions

SimpleNumericSymbolic
\( 1\)\(1.000\)\( 1 \)
\( 2\)\(1.000\)\( 1 \)
\( 3\)\(2.000\)\( 2 \)
\( 4\)\(2.000\)\( 2 \)
\( 5\)\(2.000\)\( 2 \)
\( 6\)\(2.000\)\( 2 \)
\( 7\)\(2.000\)\( 2 \)
\( 8\)\(2.000\)\( 2 \)
\( 9\)\(2.000\)\( 2 \)
\( 10\)\(3.873\)\( - 2 \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} + \frac{\sqrt{10 - 2 \sqrt{5}}}{2} + \sqrt{3} - 4 \sqrt{3} \left(\frac{1}{4} - \frac{\sqrt{5}}{4}\right) \)
\( 11\)\(3.873\)\( - 2 \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} + \frac{\sqrt{10 - 2 \sqrt{5}}}{2} + \sqrt{3} - 4 \sqrt{3} \left(\frac{1}{4} - \frac{\sqrt{5}}{4}\right) \)
\( D^2\)60.000\(60\)

Modular Data

Twist Factors

\[ \begin{pmatrix} \htmlTitle{\theta_{1}}{0} & \htmlTitle{\theta_{2}}{0} & \htmlTitle{\theta_{3}}{\frac{14}{15}} & \htmlTitle{\theta_{4}}{\frac{26}{15}} & \htmlTitle{\theta_{5}}{\frac{2}{5}} & \htmlTitle{\theta_{6}}{\frac{14}{15}} & \htmlTitle{\theta_{7}}{\frac{4}{3}} & \htmlTitle{\theta_{8}}{\frac{8}{5}} & \htmlTitle{\theta_{9}}{\frac{26}{15}} & \htmlTitle{\theta_{10}}{\frac{7}{4}} & \htmlTitle{\theta_{11}}{\frac{3}{4}} \end{pmatrix} \]

S Matrix

\[ \left(\begin{array}{lllllllllll} \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_{120}^{28} - 2 \zeta_{120}^{20} - 2 \zeta_{120}^{16} + 2 \zeta_{120}^{8} + 2 \zeta_{120}^{4} + 2} & & & & & & & & \\ \htmlTitle{S_{4; 1}}{2} & \htmlTitle{S_{4; 2}}{2} & \htmlTitle{S_{4; 3}}{-2 \zeta_{120}^{24} + 2 \zeta_{120}^{16} + 2 \zeta_{120}^{4}} & \htmlTitle{S_{4; 4}}{-4 \zeta_{120}^{28} + 2 \zeta_{120}^{20} + 2 \zeta_{120}^{16} + 2 \zeta_{120}^{12} - 2 \zeta_{120}^{4} - 2} & & & & & & & \\ \htmlTitle{S_{5; 1}}{2} & \htmlTitle{S_{5; 2}}{2} & \htmlTitle{S_{5; 3}}{-2 \zeta_{120}^{28} + 2 \zeta_{120}^{12} + 2 \zeta_{120}^{8} - 2} & \htmlTitle{S_{5; 4}}{2 \zeta_{120}^{28} - 2 \zeta_{120}^{12} - 2 \zeta_{120}^{8}} & \htmlTitle{S_{5; 5}}{2 \zeta_{120}^{28} - 2 \zeta_{120}^{12} - 2 \zeta_{120}^{8}} & & & & & & \\ \htmlTitle{S_{6; 1}}{2} & \htmlTitle{S_{6; 2}}{2} & \htmlTitle{S_{6; 3}}{-4 \zeta_{120}^{28} + 2 \zeta_{120}^{20} + 2 \zeta_{120}^{16} + 2 \zeta_{120}^{12} - 2 \zeta_{120}^{4} - 2} & \htmlTitle{S_{6; 4}}{2 \zeta_{120}^{28} + 2 \zeta_{120}^{24} - 2 \zeta_{120}^{16} - 2 \zeta_{120}^{12} - 2 \zeta_{120}^{8} - 2 \zeta_{120}^{4} + 2} & \htmlTitle{S_{6; 5}}{-2 \zeta_{120}^{28} + 2 \zeta_{120}^{12} + 2 \zeta_{120}^{8} - 2} & \htmlTitle{S_{6; 6}}{2 \zeta_{120}^{28} - 2 \zeta_{120}^{20} - 2 \zeta_{120}^{16} + 2 \zeta_{120}^{8} + 2 \zeta_{120}^{4} + 2} & & & & & \\ \htmlTitle{S_{7; 1}}{2} & \htmlTitle{S_{7; 2}}{2} & \htmlTitle{S_{7; 3}}{-2} & \htmlTitle{S_{7; 4}}{-2} & \htmlTitle{S_{7; 5}}{4} & \htmlTitle{S_{7; 6}}{-2} & \htmlTitle{S_{7; 7}}{-2} & & & & \\ \htmlTitle{S_{8; 1}}{2} & \htmlTitle{S_{8; 2}}{2} & \htmlTitle{S_{8; 3}}{2 \zeta_{120}^{28} - 2 \zeta_{120}^{12} - 2 \zeta_{120}^{8}} & \htmlTitle{S_{8; 4}}{-2 \zeta_{120}^{28} + 2 \zeta_{120}^{12} + 2 \zeta_{120}^{8} - 2} & \htmlTitle{S_{8; 5}}{-2 \zeta_{120}^{28} + 2 \zeta_{120}^{12} + 2 \zeta_{120}^{8} - 2} & \htmlTitle{S_{8; 6}}{2 \zeta_{120}^{28} - 2 \zeta_{120}^{12} - 2 \zeta_{120}^{8}} & \htmlTitle{S_{8; 7}}{4} & \htmlTitle{S_{8; 8}}{2 \zeta_{120}^{28} - 2 \zeta_{120}^{12} - 2 \zeta_{120}^{8}} & & & \\ \htmlTitle{S_{9; 1}}{2} & \htmlTitle{S_{9; 2}}{2} & \htmlTitle{S_{9; 3}}{2 \zeta_{120}^{28} + 2 \zeta_{120}^{24} - 2 \zeta_{120}^{16} - 2 \zeta_{120}^{12} - 2 \zeta_{120}^{8} - 2 \zeta_{120}^{4} + 2} & \htmlTitle{S_{9; 4}}{2 \zeta_{120}^{28} - 2 \zeta_{120}^{20} - 2 \zeta_{120}^{16} + 2 \zeta_{120}^{8} + 2 \zeta_{120}^{4} + 2} & \htmlTitle{S_{9; 5}}{2 \zeta_{120}^{28} - 2 \zeta_{120}^{12} - 2 \zeta_{120}^{8}} & \htmlTitle{S_{9; 6}}{-2 \zeta_{120}^{24} + 2 \zeta_{120}^{16} + 2 \zeta_{120}^{4}} & \htmlTitle{S_{9; 7}}{-2} & \htmlTitle{S_{9; 8}}{-2 \zeta_{120}^{28} + 2 \zeta_{120}^{12} + 2 \zeta_{120}^{8} - 2} & \htmlTitle{S_{9; 9}}{-4 \zeta_{120}^{28} + 2 \zeta_{120}^{20} + 2 \zeta_{120}^{16} + 2 \zeta_{120}^{12} - 2 \zeta_{120}^{4} - 2} & & \\ \htmlTitle{S_{10; 1}}{-3 \zeta_{120}^{30} - 4 \zeta_{120}^{26} + 2 \zeta_{120}^{22} + 2 \zeta_{120}^{18} + 4 \zeta_{120}^{14} + 2 \zeta_{120}^{10} - 2 \zeta_{120}^{2}} & \htmlTitle{S_{10; 2}}{3 \zeta_{120}^{30} + 4 \zeta_{120}^{26} - 2 \zeta_{120}^{22} - 2 \zeta_{120}^{18} - 4 \zeta_{120}^{14} - 2 \zeta_{120}^{10} + 2 \zeta_{120}^{2}} & \htmlTitle{S_{10; 3}}{0} & \htmlTitle{S_{10; 4}}{0} & \htmlTitle{S_{10; 5}}{0} & \htmlTitle{S_{10; 6}}{0} & \htmlTitle{S_{10; 7}}{0} & \htmlTitle{S_{10; 8}}{0} & \htmlTitle{S_{10; 9}}{0} & \htmlTitle{S_{10; 10}}{-3 \zeta_{120}^{30} - 4 \zeta_{120}^{26} + 2 \zeta_{120}^{22} + 2 \zeta_{120}^{18} + 4 \zeta_{120}^{14} + 2 \zeta_{120}^{10} - 2 \zeta_{120}^{2}} & \\ \htmlTitle{S_{11; 1}}{-3 \zeta_{120}^{30} - 4 \zeta_{120}^{26} + 2 \zeta_{120}^{22} + 2 \zeta_{120}^{18} + 4 \zeta_{120}^{14} + 2 \zeta_{120}^{10} - 2 \zeta_{120}^{2}} & \htmlTitle{S_{11; 2}}{3 \zeta_{120}^{30} + 4 \zeta_{120}^{26} - 2 \zeta_{120}^{22} - 2 \zeta_{120}^{18} - 4 \zeta_{120}^{14} - 2 \zeta_{120}^{10} + 2 \zeta_{120}^{2}} & \htmlTitle{S_{11; 3}}{0} & \htmlTitle{S_{11; 4}}{0} & \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}}{3 \zeta_{120}^{30} + 4 \zeta_{120}^{26} - 2 \zeta_{120}^{22} - 2 \zeta_{120}^{18} - 4 \zeta_{120}^{14} - 2 \zeta_{120}^{10} + 2 \zeta_{120}^{2}} & \htmlTitle{S_{11; 11}}{-3 \zeta_{120}^{30} - 4 \zeta_{120}^{26} + 2 \zeta_{120}^{22} + 2 \zeta_{120}^{18} + 4 \zeta_{120}^{14} + 2 \zeta_{120}^{10} - 2 \zeta_{120}^{2}}\end{array}\right) \]

Central Charge

\[c = 14 \]