SO(5) 2 | VerlindeDB

\(\operatorname{SO}(5)_{2}\): \( B_{2} \) at level \(2\)

Fusion Ring

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

Frobenius-Perron Dimensions

SimpleNumericSymbolic
\( 1\)\(1.000\)\( 1 \)
\( 2\)\(1.000\)\( 1 \)
\( 3\)\(2.000\)\( 2 \)
\( 4\)\(2.000\)\( 2 \)
\( 5\)\(2.236\)\( \sqrt{5} \)
\( 6\)\(2.236\)\( \sqrt{5} \)
\( D^2\)20.000\(20\)

Modular Data

Twist Factors

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

S Matrix

\[ \left(\begin{array}{llllll} \htmlTitle{S_{1; 1}}{1} & & & & & \\ \htmlTitle{S_{2; 1}}{1} & \htmlTitle{S_{2; 2}}{1} & & & & \\ \htmlTitle{S_{3; 1}}{2} & \htmlTitle{S_{3; 2}}{2} & \htmlTitle{S_{3; 3}}{-2 \zeta_{40}^{12} + 2 \zeta_{40}^{8}} & & & \\ \htmlTitle{S_{4; 1}}{2} & \htmlTitle{S_{4; 2}}{2} & \htmlTitle{S_{4; 3}}{2 \zeta_{40}^{12} - 2 \zeta_{40}^{8} - 2} & \htmlTitle{S_{4; 4}}{-2 \zeta_{40}^{12} + 2 \zeta_{40}^{8}} & & \\ \htmlTitle{S_{5; 1}}{-2 \zeta_{40}^{12} + 2 \zeta_{40}^{8} + 1} & \htmlTitle{S_{5; 2}}{2 \zeta_{40}^{12} - 2 \zeta_{40}^{8} - 1} & \htmlTitle{S_{5; 3}}{0} & \htmlTitle{S_{5; 4}}{0} & \htmlTitle{S_{5; 5}}{-2 \zeta_{40}^{12} + 2 \zeta_{40}^{8} + 1} & \\ \htmlTitle{S_{6; 1}}{-2 \zeta_{40}^{12} + 2 \zeta_{40}^{8} + 1} & \htmlTitle{S_{6; 2}}{2 \zeta_{40}^{12} - 2 \zeta_{40}^{8} - 1} & \htmlTitle{S_{6; 3}}{0} & \htmlTitle{S_{6; 4}}{0} & \htmlTitle{S_{6; 5}}{2 \zeta_{40}^{12} - 2 \zeta_{40}^{8} - 1} & \htmlTitle{S_{6; 6}}{-2 \zeta_{40}^{12} + 2 \zeta_{40}^{8} + 1}\end{array}\right) \]

Central Charge

\[c = 4 \]