10 109 Quantum Invariants: Difference between revisions
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Revision as of 19:18, 4 December 2005
A1 Invariants.
| Weight | Invariant |
|---|---|
| 1 | [math]\displaystyle{ -q^{11}+2 q^9-4 q^7+4 q^5-2 q^3+2 q+2 q^{-1} -2 q^{-3} +4 q^{-5} -4 q^{-7} +2 q^{-9} - q^{-11} }[/math] |
| 2 | [math]\displaystyle{ q^{32}-2 q^{30}+7 q^{26}-10 q^{24}-6 q^{22}+26 q^{20}-14 q^{18}-27 q^{16}+38 q^{14}-38 q^{10}+26 q^8+16 q^6-26 q^4+21-26 q^{-4} +16 q^{-6} +26 q^{-8} -38 q^{-10} +38 q^{-14} -27 q^{-16} -14 q^{-18} +26 q^{-20} -6 q^{-22} -10 q^{-24} +7 q^{-26} -2 q^{-30} + q^{-32} }[/math] |
| 3 | [math]\displaystyle{ -q^{63}+2 q^{61}-3 q^{57}-q^{55}+9 q^{53}+4 q^{51}-23 q^{49}-13 q^{47}+44 q^{45}+41 q^{43}-62 q^{41}-100 q^{39}+65 q^{37}+172 q^{35}-28 q^{33}-238 q^{31}-52 q^{29}+280 q^{27}+139 q^{25}-267 q^{23}-226 q^{21}+215 q^{19}+277 q^{17}-135 q^{15}-291 q^{13}+55 q^{11}+264 q^9+30 q^7-219 q^5-98 q^3+162 q+162 q^{-1} -98 q^{-3} -219 q^{-5} +30 q^{-7} +264 q^{-9} +55 q^{-11} -291 q^{-13} -135 q^{-15} +277 q^{-17} +215 q^{-19} -226 q^{-21} -267 q^{-23} +139 q^{-25} +280 q^{-27} -52 q^{-29} -238 q^{-31} -28 q^{-33} +172 q^{-35} +65 q^{-37} -100 q^{-39} -62 q^{-41} +41 q^{-43} +44 q^{-45} -13 q^{-47} -23 q^{-49} +4 q^{-51} +9 q^{-53} - q^{-55} -3 q^{-57} +2 q^{-61} - q^{-63} }[/math] |
A2 Invariants.
| Weight | Invariant |
|---|---|
| 1,0 | [math]\displaystyle{ -q^{14}+q^{12}-3 q^{10}+q^8-q^4+5 q^2-1+5 q^{-2} - q^{-4} + q^{-8} -3 q^{-10} + q^{-12} - q^{-14} }[/math] |
| 1,1 | [math]\displaystyle{ q^{44}-4 q^{42}+12 q^{40}-28 q^{38}+60 q^{36}-116 q^{34}+204 q^{32}-334 q^{30}+514 q^{28}-738 q^{26}+976 q^{24}-1190 q^{22}+1334 q^{20}-1352 q^{18}+1186 q^{16}-840 q^{14}+312 q^{12}+332 q^{10}-1030 q^8+1690 q^6-2220 q^4+2582 q^2-2694+2582 q^{-2} -2220 q^{-4} +1690 q^{-6} -1030 q^{-8} +332 q^{-10} +312 q^{-12} -840 q^{-14} +1186 q^{-16} -1352 q^{-18} +1334 q^{-20} -1190 q^{-22} +976 q^{-24} -738 q^{-26} +514 q^{-28} -334 q^{-30} +204 q^{-32} -116 q^{-34} +60 q^{-36} -28 q^{-38} +12 q^{-40} -4 q^{-42} + q^{-44} }[/math] |
| 2,0 | [math]\displaystyle{ q^{38}-q^{36}+4 q^{32}-3 q^{30}-5 q^{28}+7 q^{26}+3 q^{24}-9 q^{22}-7 q^{20}+9 q^{18}+5 q^{16}-19 q^{14}+2 q^{12}+14 q^{10}-8 q^8-6 q^6+12 q^4+7 q^2-6+7 q^{-2} +12 q^{-4} -6 q^{-6} -8 q^{-8} +14 q^{-10} +2 q^{-12} -19 q^{-14} +5 q^{-16} +9 q^{-18} -7 q^{-20} -9 q^{-22} +3 q^{-24} +7 q^{-26} -5 q^{-28} -3 q^{-30} +4 q^{-32} - q^{-36} + q^{-38} }[/math] |
A3 Invariants.
| Weight | Invariant |
|---|---|
| 0,1,0 | [math]\displaystyle{ q^{34}-2 q^{32}+q^{30}+5 q^{28}-9 q^{26}+2 q^{24}+15 q^{22}-22 q^{20}+2 q^{18}+23 q^{16}-32 q^{14}-q^{12}+22 q^{10}-22 q^8-3 q^6+19 q^4+4 q^2+4 q^{-2} +19 q^{-4} -3 q^{-6} -22 q^{-8} +22 q^{-10} - q^{-12} -32 q^{-14} +23 q^{-16} +2 q^{-18} -22 q^{-20} +15 q^{-22} +2 q^{-24} -9 q^{-26} +5 q^{-28} + q^{-30} -2 q^{-32} + q^{-34} }[/math] |
| 1,0,0 | [math]\displaystyle{ -q^{17}+q^{15}-4 q^{13}+2 q^{11}-4 q^9+2 q^7-q^5+4 q^3+3 q+3 q^{-1} +4 q^{-3} - q^{-5} +2 q^{-7} -4 q^{-9} +2 q^{-11} -4 q^{-13} + q^{-15} - q^{-17} }[/math] |
| 1,0,1 | [math]\displaystyle{ q^{56}-4 q^{54}+10 q^{52}-14 q^{50}+7 q^{48}+23 q^{46}-72 q^{44}+110 q^{42}-85 q^{40}-44 q^{38}+252 q^{36}-425 q^{34}+405 q^{32}-93 q^{30}-430 q^{28}+923 q^{26}-1076 q^{24}+723 q^{22}+48 q^{20}-926 q^{18}+1449 q^{16}-1414 q^{14}+762 q^{12}+89 q^{10}-756 q^8+914 q^6-568 q^4+142 q^2+113+142 q^{-2} -568 q^{-4} +914 q^{-6} -756 q^{-8} +89 q^{-10} +762 q^{-12} -1414 q^{-14} +1449 q^{-16} -926 q^{-18} +48 q^{-20} +723 q^{-22} -1076 q^{-24} +923 q^{-26} -430 q^{-28} -93 q^{-30} +405 q^{-32} -425 q^{-34} +252 q^{-36} -44 q^{-38} -85 q^{-40} +110 q^{-42} -72 q^{-44} +23 q^{-46} +7 q^{-48} -14 q^{-50} +10 q^{-52} -4 q^{-54} + q^{-56} }[/math] |
A4 Invariants.
| Weight | Invariant |
|---|---|
| 0,1,0,0 | [math]\displaystyle{ q^{40}-q^{38}+5 q^{34}-3 q^{32}-4 q^{30}+13 q^{28}-3 q^{26}-15 q^{24}+10 q^{22}+9 q^{20}-25 q^{18}-14 q^{16}+13 q^{14}-7 q^{12}-28 q^{10}+9 q^8+30 q^6-14 q^4+6 q^2+46+6 q^{-2} -14 q^{-4} +30 q^{-6} +9 q^{-8} -28 q^{-10} -7 q^{-12} +13 q^{-14} -14 q^{-16} -25 q^{-18} +9 q^{-20} +10 q^{-22} -15 q^{-24} -3 q^{-26} +13 q^{-28} -4 q^{-30} -3 q^{-32} +5 q^{-34} - q^{-38} + q^{-40} }[/math] |
| 1,0,0,0 | [math]\displaystyle{ -q^{20}+q^{18}-4 q^{16}+q^{14}-3 q^{12}-2 q^{10}+q^8-q^6+5 q^4+2 q^2+7+2 q^{-2} +5 q^{-4} - q^{-6} + q^{-8} -2 q^{-10} -3 q^{-12} + q^{-14} -4 q^{-16} + q^{-18} - q^{-20} }[/math] |
B2 Invariants.
| Weight | Invariant |
|---|---|
| 0,1 | [math]\displaystyle{ -q^{34}+2 q^{32}-5 q^{30}+9 q^{28}-15 q^{26}+22 q^{24}-29 q^{22}+34 q^{20}-36 q^{18}+31 q^{16}-24 q^{14}+11 q^{12}+4 q^{10}-22 q^8+41 q^6-53 q^4+66 q^2-66+66 q^{-2} -53 q^{-4} +41 q^{-6} -22 q^{-8} +4 q^{-10} +11 q^{-12} -24 q^{-14} +31 q^{-16} -36 q^{-18} +34 q^{-20} -29 q^{-22} +22 q^{-24} -15 q^{-26} +9 q^{-28} -5 q^{-30} +2 q^{-32} - q^{-34} }[/math] |
| 1,0 | [math]\displaystyle{ q^{56}-2 q^{52}-2 q^{50}+3 q^{48}+7 q^{46}-12 q^{42}-9 q^{40}+12 q^{38}+22 q^{36}-3 q^{34}-31 q^{32}-15 q^{30}+28 q^{28}+29 q^{26}-16 q^{24}-39 q^{22}-4 q^{20}+34 q^{18}+15 q^{16}-26 q^{14}-22 q^{12}+17 q^{10}+24 q^8-6 q^6-22 q^4+6 q^2+27+6 q^{-2} -22 q^{-4} -6 q^{-6} +24 q^{-8} +17 q^{-10} -22 q^{-12} -26 q^{-14} +15 q^{-16} +34 q^{-18} -4 q^{-20} -39 q^{-22} -16 q^{-24} +29 q^{-26} +28 q^{-28} -15 q^{-30} -31 q^{-32} -3 q^{-34} +22 q^{-36} +12 q^{-38} -9 q^{-40} -12 q^{-42} +7 q^{-46} +3 q^{-48} -2 q^{-50} -2 q^{-52} + q^{-56} }[/math] |
D4 Invariants.
| Weight | Invariant |
|---|---|
| 1,0,0,0 | [math]\displaystyle{ q^{46}-2 q^{44}+3 q^{42}-4 q^{40}+8 q^{38}-12 q^{36}+14 q^{34}-17 q^{32}+24 q^{30}-28 q^{28}+26 q^{26}-27 q^{24}+26 q^{22}-24 q^{20}+8 q^{18}-11 q^{16}-3 q^{14}+11 q^{12}-28 q^{10}+31 q^8-34 q^6+56 q^4-43 q^2+58-43 q^{-2} +56 q^{-4} -34 q^{-6} +31 q^{-8} -28 q^{-10} +11 q^{-12} -3 q^{-14} -11 q^{-16} +8 q^{-18} -24 q^{-20} +26 q^{-22} -27 q^{-24} +26 q^{-26} -28 q^{-28} +24 q^{-30} -17 q^{-32} +14 q^{-34} -12 q^{-36} +8 q^{-38} -4 q^{-40} +3 q^{-42} -2 q^{-44} + q^{-46} }[/math] |
G2 Invariants.
| Weight | Invariant |
|---|---|
| 1,0 | [math]\displaystyle{ q^{80}-2 q^{78}+5 q^{76}-8 q^{74}+9 q^{72}-8 q^{70}+q^{68}+14 q^{66}-32 q^{64}+51 q^{62}-62 q^{60}+51 q^{58}-20 q^{56}-39 q^{54}+113 q^{52}-171 q^{50}+187 q^{48}-138 q^{46}+19 q^{44}+124 q^{42}-249 q^{40}+297 q^{38}-239 q^{36}+89 q^{34}+90 q^{32}-231 q^{30}+264 q^{28}-177 q^{26}+13 q^{24}+150 q^{22}-232 q^{20}+187 q^{18}-37 q^{16}-151 q^{14}+301 q^{12}-336 q^{10}+248 q^8-53 q^6-170 q^4+353 q^2-417+353 q^{-2} -170 q^{-4} -53 q^{-6} +248 q^{-8} -336 q^{-10} +301 q^{-12} -151 q^{-14} -37 q^{-16} +187 q^{-18} -232 q^{-20} +150 q^{-22} +13 q^{-24} -177 q^{-26} +264 q^{-28} -231 q^{-30} +90 q^{-32} +89 q^{-34} -239 q^{-36} +297 q^{-38} -249 q^{-40} +124 q^{-42} +19 q^{-44} -138 q^{-46} +187 q^{-48} -171 q^{-50} +113 q^{-52} -39 q^{-54} -20 q^{-56} +51 q^{-58} -62 q^{-60} +51 q^{-62} -32 q^{-64} +14 q^{-66} + q^{-68} -8 q^{-70} +9 q^{-72} -8 q^{-74} +5 q^{-76} -2 q^{-78} + q^{-80} }[/math] |
