FR209,2
Fusion Rules
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The fusion rules are invariant under the group generated by the following permutations:
{(2 3),(8 9)}
The following elements form non-trivial sub fusion rings
Elements |
SubRing |
{1,2} |
Z2: FR12,0 |
{1,3} |
Z2: FR12,0 |
{1,4} |
Z2: FR12,0 |
{1,4,5} |
Rep(D3): FR23,0 |
{1,2,3,4} |
Z2×Z2: FR14,0 |
{1,2,3,4,5,6} |
\(\left.\mathbb{Z}_2\text{×Rep(}D_3\right):\ \text{FR}^{6,0}_{2}\) |
Frobenius-Perron Dimensions
Particle |
Numeric |
Symbolic |
1 |
1. |
1 |
2 |
1. |
1 |
3 |
1. |
1 |
4 |
1. |
1 |
5 |
2. |
2 |
6 |
2. |
2 |
7 |
4. |
4 |
8 |
4. |
4 |
9 |
4. |
4 |
DFP2 |
60. |
60 |
Characters
The symbolic character table is the following
111111111121111−11−1−1−131111−1−11−1−1411111−1−111522−1−1200−1−1622−1−1−2001174−1−220000084−11−1000i3−i394−11−1000−i3i3
The numeric character table is the following
11.0001.0001.0001.0001.0001.0001.0001.0001.00021.0001.0001.0001.000−1.0001.000−1.000−1.000−1.00031.0001.0001.0001.000−1.000−1.0001.000−1.000−1.00041.0001.0001.0001.0001.000−1.000−1.0001.0001.00052.0002.000−1.000−1.0002.00000−1.000−1.00062.0002.000−1.000−1.000−2.000001.0001.00074.000−1.000−2.0002.0000000084.000−1.0001.000−1.0000001.732i−1.732i94.000−1.0001.000−1.000000−1.732i1.732i
Representations of SL2(Z)
This fusion ring does not provide any representations of SL2(Z).
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
Data
Download links for numeric data: