FR27,0
Fusion Rules
123456721435763412576432156755551+2+3+46+76+767766+71+4+5+72+3+5+676676+72+3+5+61+4+5+7
The fusion rules are invariant under the group generated by the following permutations:
{(2 3)}
The following particles form non-trivial sub fusion rings
Particles |
SubRing |
{1,2} |
Z2: FR12,0 |
{1,3} |
Z2: FR12,0 |
{1,4} |
Z2: FR12,0 |
{1,2,3,4} |
Z2×Z2: FR14,0 |
{1,2,3,4,5} |
Rep(D4): FR15,0 |
Quantum Dimensions
Particle |
Numeric |
Symbolic |
1 |
1. |
1 |
2 |
1. |
1 |
3 |
1. |
1 |
4 |
1. |
1 |
5 |
2. |
2 |
6 |
2.56155 |
21(1+17) |
7 |
2.56155 |
21(1+17) |
DFP2 |
21.1231 |
8+21(1+17)2 |
Characters
The symbolic character table is the following
111111112111−11−1−141111−11−13111−1−1−11522−20000621(1+17)21(1−17)010−20721(1+17)21(1−17)0−1020
The numeric character table is the following
11.0001.0001.0001.0001.0001.0001.00021.0001.0001.000−1.0001.000−1.000−1.00041.0001.0001.0001.000−1.0001.000−1.00031.0001.0001.000−1.000−1.000−1.0001.00052.0002.000−2.000000062.562−1.56201.0000−2.000072.562−1.5620−1.00002.0000
Modular Data
This fusion ring does not have any matching S-and T-matrices.
Adjoint Subring
The adjoint subring is the ring itself.
The upper central series is trivial.
Universal grading
This fusion ring allows only the trivial grading.
Categorifications
This fusion ring has no categorifications because of the d-number criterion.
Data
Download links for numeric data: