Below is a collected list of low(ish) rank Verlinde categories. Click on the names for more information, including the fusion rules, Frobenius-Perron dimensions of the simple objects, and modular data. Please see the conventions page for how to use the site. The goal is to be a kind of landing page for quick references to these categories for researchers and anyone interested.

For questions and/or suggestions, please email abaxi [AT] tamu [DOT] edu or open a GitHub issue. Replace the bracketed terms with the obvious replacements.

CategoryRank$D^2$Cartan TypeLevel
\(\operatorname{SU}(2)_{1}\)22.000\( A_{1} \)1
\(\operatorname{E}_{8}(2)\)34.000\( E_{8} \)2
\(\operatorname{SO}(11)_{1}\)34.000\( B_{5} \)1
\(\operatorname{SO}(13)_{1}\)34.000\( B_{6} \)1
\(\operatorname{SO}(15)_{1}\)34.000\( B_{7} \)1
\(\operatorname{SO}(17)_{1}\)34.000\( B_{8} \)1
\(\operatorname{SO}(19)_{1}\)34.000\( B_{9} \)1
\(\operatorname{SO}(21)_{1}\)34.000\( B_{10} \)1
\(\operatorname{SO}(23)_{1}\)34.000\( B_{11} \)1
\(\operatorname{SO}(25)_{1}\)34.000\( B_{12} \)1
\(\operatorname{SO}(27)_{1}\)34.000\( B_{13} \)1
\(\operatorname{SO}(29)_{1}\)34.000\( B_{14} \)1
\(\operatorname{SO}(31)_{1}\)34.000\( B_{15} \)1
\(\operatorname{SO}(33)_{1}\)34.000\( B_{16} \)1
\(\operatorname{SO}(35)_{1}\)34.000\( B_{17} \)1
\(\operatorname{SO}(37)_{1}\)34.000\( B_{18} \)1
\(\operatorname{SO}(5)_{1}\)34.000\( B_{2} \)1
\(\operatorname{SO}(7)_{1}\)34.000\( B_{3} \)1
\(\operatorname{SO}(9)_{1}\)34.000\( B_{4} \)1
\(\operatorname{SU}(2)_{2}\)34.000\( A_{1} \)2
\(\operatorname{G}_{2}(2)\)419.234\( G_{2} \)2
\(\operatorname{SU}(2)_{3}\)47.236\( A_{1} \)3
\(\operatorname{E}_{8}(3)\)534.646\( E_{8} \)3
\(\operatorname{F}_{4}(2)\)534.646\( F_{4} \)2
\(\operatorname{SU}(2)_{4}\)512.000\( A_{1} \)4
\(\operatorname{E}_{7}(2)\)614.472\( E_{7} \)2
\(\operatorname{G}_{2}(3)\)6100.617\( G_{2} \)3
\(\operatorname{SO}(5)_{2}\)620.000\( B_{2} \)2
\(\operatorname{Sp}(4)_{2}\)620.000\( C_{2} \)2
\(\operatorname{SU}(2)_{5}\)618.592\( A_{1} \)5
\(\operatorname{SU}(3)_{2}\)610.854\( A_{2} \)2
\(\operatorname{SO}(7)_{2}\)728.000\( B_{3} \)2
\(\operatorname{SU}(2)_{6}\)727.314\( A_{1} \)6
\(\operatorname{SO}(9)_{2}\)836.000\( B_{4} \)2
\(\operatorname{SU}(2)_{7}\)838.469\( A_{1} \)7
\(\operatorname{E}_{6}(2)\)927.888\( E_{6} \)2
\(\operatorname{F}_{4}(3)\)9475.151\( F_{4} \)3
\(\operatorname{G}_{2}(4)\)9475.151\( G_{2} \)4
\(\operatorname{SO}(11)_{2}\)944.000\( B_{5} \)2
\(\operatorname{SU}(2)_{8}\)952.361\( A_{1} \)8
\(\operatorname{E}_{8}(4)\)10499.210\( E_{8} \)4
\(\operatorname{SO}(13)_{2}\)1052.000\( B_{6} \)2
\(\operatorname{SO}(5)_{3}\)1089.569\( B_{2} \)3
\(\operatorname{SO}(6)_{2}\)1024.000\( D_{3} \)2
\(\operatorname{Sp}(4)_{3}\)1089.569\( C_{2} \)3
\(\operatorname{Sp}(6)_{2}\)1089.569\( C_{3} \)2
\(\operatorname{SU}(2)_{9}\)1069.293\( A_{1} \)9
\(\operatorname{SU}(3)_{3}\)1036.000\( A_{2} \)3
\(\operatorname{SO}(15)_{2}\)1160.000\( B_{7} \)2
\(\operatorname{SO}(8)_{2}\)1132.000\( D_{4} \)2
\(\operatorname{SU}(2)_{10}\)1189.569\( A_{1} \)10
\(\operatorname{E}_{7}(3)\)12201.234\( E_{7} \)3
\(\operatorname{G}_{2}(5)\)121996.556\( G_{2} \)5
\(\operatorname{SO}(10)_{2}\)1240.000\( D_{5} \)2
\(\operatorname{SO}(17)_{2}\)1268.000\( B_{8} \)2
\(\operatorname{SU}(2)_{11}\)12113.494\( A_{1} \)11
\(\operatorname{SO}(12)_{2}\)1348.000\( D_{6} \)2
\(\operatorname{SO}(19)_{2}\)1376.000\( B_{9} \)2
\(\operatorname{SO}(7)_{3}\)13210.193\( B_{3} \)3
\(\operatorname{SU}(2)_{12}\)13141.370\( A_{1} \)12
\(\operatorname{SO}(14)_{2}\)1456.000\( D_{7} \)2
\(\operatorname{SO}(21)_{2}\)1484.000\( B_{10} \)2
\(\operatorname{SU}(2)_{13}\)14173.502\( A_{1} \)13
\(\operatorname{SO}(5)_{4}\)15345.655\( B_{2} \)4
\(\operatorname{Sp}(4)_{4}\)15345.655\( C_{2} \)4
\(\operatorname{Sp}(8)_{2}\)15345.655\( C_{4} \)2
\(\operatorname{SU}(2)_{14}\)15210.193\( A_{1} \)14
\(\operatorname{SU}(3)_{4}\)15106.027\( A_{2} \)4
\(\operatorname{F}_{4}(4)\)167402.794\( F_{4} \)4
\(\operatorname{G}_{2}(6)\)167505.993\( G_{2} \)6
\(\operatorname{SO}(9)_{3}\)16408.635\( B_{4} \)3
\(\operatorname{SU}(2)_{15}\)16251.748\( A_{1} \)15
\(\operatorname{SU}(2)_{16}\)17298.471\( A_{1} \)16
\(\operatorname{SU}(2)_{17}\)18350.665\( A_{1} \)17
\(\operatorname{SU}(2)_{18}\)19408.635\( A_{1} \)18
\(\operatorname{E}_{6}(3)\)20426.246\( E_{6} \)3
\(\operatorname{G}_{2}(7)\)2025520.068\( G_{2} \)7
\(\operatorname{SO}(6)_{3}\)20141.370\( D_{3} \)3
\(\operatorname{Sp}(6)_{3}\)201074.957\( C_{3} \)3
\(\operatorname{SU}(2)_{19}\)20472.683\( A_{1} \)19
\(\operatorname{SO}(5)_{5}\)211162.522\( B_{2} \)5
\(\operatorname{Sp}(10)_{2}\)211162.522\( C_{5} \)2
\(\operatorname{Sp}(4)_{5}\)211162.522\( C_{2} \)5
\(\operatorname{SU}(2)_{20}\)21543.116\( A_{1} \)20
\(\operatorname{SU}(3)_{5}\)21279.765\( A_{2} \)5
\(\operatorname{SO}(7)_{4}\)221479.852\( B_{3} \)4
\(\operatorname{SU}(2)_{21}\)22620.235\( A_{1} \)21
\(\operatorname{SU}(2)_{22}\)23704.346\( A_{1} \)22
\(\operatorname{SO}(8)_{3}\)24298.471\( D_{4} \)3
\(\operatorname{SU}(2)_{23}\)24795.752\( A_{1} \)23
\(\operatorname{E}_{7}(4)\)254106.762\( E_{7} \)4
\(\operatorname{F}_{4}(5)\)25117593.688\( F_{4} \)5
\(\operatorname{G}_{2}(8)\)2579365.073\( G_{2} \)8
\(\operatorname{SU}(2)_{24}\)25894.757\( A_{1} \)24
\(\operatorname{SU}(2)_{25}\)261001.665\( A_{1} \)25
\(\operatorname{SU}(2)_{26}\)271116.780\( A_{1} \)26
\(\operatorname{SO}(10)_{3}\)28543.116\( D_{5} \)3
\(\operatorname{SO}(5)_{6}\)283473.651\( B_{2} \)6
\(\operatorname{Sp}(12)_{2}\)283473.651\( C_{6} \)2
\(\operatorname{Sp}(4)_{6}\)283473.651\( C_{2} \)6
\(\operatorname{SU}(2)_{27}\)281240.406\( A_{1} \)27
\(\operatorname{SU}(3)_{6}\)28671.560\( A_{2} \)6
\(\operatorname{SU}(2)_{28}\)291372.847\( A_{1} \)28
\(\operatorname{G}_{2}(9)\)30228134.999\( G_{2} \)9
\(\operatorname{SO}(9)_{4}\)304801.503\( B_{4} \)4
\(\operatorname{SU}(2)_{29}\)301514.407\( A_{1} \)29
\(\operatorname{SU}(2)_{30}\)311665.390\( A_{1} \)30
\(\operatorname{SO}(12)_{3}\)32894.757\( D_{6} \)3
\(\operatorname{SU}(2)_{31}\)321826.100\( A_{1} \)31
\(\operatorname{SU}(2)_{32}\)331996.840\( A_{1} \)32
\(\operatorname{SO}(7)_{5}\)349389.869\( B_{3} \)5
\(\operatorname{SU}(2)_{33}\)342177.916\( A_{1} \)33
\(\operatorname{SO}(6)_{4}\)35746.039\( D_{3} \)4
\(\operatorname{Sp}(6)_{4}\)3511045.289\( C_{3} \)4
\(\operatorname{Sp}(8)_{3}\)3511045.289\( C_{4} \)3
\(\operatorname{SU}(2)_{34}\)352369.630\( A_{1} \)34
\(\operatorname{SO}(14)_{3}\)361372.847\( D_{7} \)3
\(\operatorname{SO}(5)_{7}\)369389.869\( B_{2} \)7
\(\operatorname{Sp}(4)_{7}\)369389.869\( C_{2} \)7
\(\operatorname{SU}(2)_{35}\)362572.287\( A_{1} \)35
\(\operatorname{SU}(3)_{7}\)361487.902\( A_{2} \)7
\(\operatorname{SU}(2)_{36}\)372786.190\( A_{1} \)36
\(\operatorname{SU}(2)_{37}\)383011.644\( A_{1} \)37
\(\operatorname{F}_{4}(6)\)391803237.970\( F_{4} \)6
\(\operatorname{SU}(2)_{38}\)393248.953\( A_{1} \)38