SO(19) 1 | VerlindeDB

\(\operatorname{SO}(19)_{1}\): \( B_{9} \) at level \(1\)

Fusion Ring

\[ \begin{array}{lll} \htmlTitle{1\otimes 1}{1} & & \\ \htmlTitle{2\otimes 1}{2} & \htmlTitle{2\otimes 2}{1} & \\ \htmlTitle{3\otimes 1}{3} & \htmlTitle{3\otimes 2}{3} & \htmlTitle{3\otimes 3}{1 \oplus 2} \\ \end{array} \]

Frobenius-Perron Dimensions

SimpleNumericSymbolic
\( 1\)\(1.000\)\( 1 \)
\( 2\)\(1.000\)\( 1 \)
\( 3\)\(1.414\)\( \sqrt{2} \)
\( D^2\)4.000\(4\)

Modular Data

Twist Factors

\[ \begin{pmatrix} \htmlTitle{\theta_{1}}{0} & \htmlTitle{\theta_{2}}{1} & \htmlTitle{\theta_{3}}{\frac{3}{8}} \end{pmatrix} \]

S Matrix

\[ \left(\begin{array}{lll} \htmlTitle{S_{1; 1}}{1} & & \\ \htmlTitle{S_{2; 1}}{1} & \htmlTitle{S_{2; 2}}{1} & \\ \htmlTitle{S_{3; 1}}{-\zeta_{144}^{30} + \zeta_{144}^{18} + \zeta_{144}^{6}} & \htmlTitle{S_{3; 2}}{\zeta_{144}^{30} - \zeta_{144}^{18} - \zeta_{144}^{6}} & \htmlTitle{S_{3; 3}}{0}\end{array}\right) \]

Central Charge

\[c = \frac{19}{2} \]