8 10 Quantum Invariants: Difference between revisions
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Revision as of 18:59, 4 December 2005
A1 Invariants.
| Weight | Invariant |
|---|---|
| 1 | [math]\displaystyle{ -q^5+q^3-q+2 q^{-1} + q^{-3} + q^{-5} + q^{-7} -2 q^{-9} + q^{-11} - q^{-13} }[/math] |
| 2 | [math]\displaystyle{ q^{16}-q^{14}-2 q^{12}+3 q^{10}-5 q^6+3 q^4+3 q^2-5+2 q^{-2} +5 q^{-4} -2 q^{-6} +4 q^{-10} + q^{-12} -2 q^{-14} - q^{-16} +4 q^{-18} -4 q^{-20} -4 q^{-22} +6 q^{-24} -2 q^{-26} -4 q^{-28} +3 q^{-30} - q^{-34} + q^{-36} }[/math] |
| 3 | [math]\displaystyle{ -q^{33}+q^{31}+2 q^{29}-4 q^{25}-2 q^{23}+6 q^{21}+5 q^{19}-6 q^{17}-10 q^{15}+3 q^{13}+13 q^{11}+q^9-15 q^7-6 q^5+12 q^3+12 q-11 q^{-1} -11 q^{-3} +8 q^{-5} +16 q^{-7} -3 q^{-9} -13 q^{-11} +2 q^{-13} +14 q^{-15} + q^{-17} -10 q^{-19} -3 q^{-21} +6 q^{-23} +8 q^{-25} -4 q^{-27} -11 q^{-29} -4 q^{-31} +14 q^{-33} +6 q^{-35} -13 q^{-37} -13 q^{-39} +13 q^{-41} +13 q^{-43} -10 q^{-45} -13 q^{-47} +4 q^{-49} +11 q^{-51} - q^{-53} -6 q^{-55} + q^{-57} +3 q^{-59} - q^{-63} + q^{-67} - q^{-69} }[/math] |
| 4 | [math]\displaystyle{ q^{56}-q^{54}-2 q^{52}+q^{48}+6 q^{46}-6 q^{42}-6 q^{40}-4 q^{38}+15 q^{36}+12 q^{34}-2 q^{32}-16 q^{30}-25 q^{28}+9 q^{26}+26 q^{24}+24 q^{22}-4 q^{20}-45 q^{18}-22 q^{16}+11 q^{14}+45 q^{12}+32 q^{10}-33 q^8-46 q^6-26 q^4+37 q^2+60+ q^{-2} -40 q^{-4} -49 q^{-6} +13 q^{-8} +60 q^{-10} +25 q^{-12} -26 q^{-14} -52 q^{-16} - q^{-18} +46 q^{-20} +28 q^{-22} -16 q^{-24} -42 q^{-26} -9 q^{-28} +27 q^{-30} +29 q^{-32} -4 q^{-34} -30 q^{-36} -22 q^{-38} +5 q^{-40} +32 q^{-42} +21 q^{-44} -7 q^{-46} -40 q^{-48} -31 q^{-50} +28 q^{-52} +46 q^{-54} +27 q^{-56} -41 q^{-58} -66 q^{-60} +3 q^{-62} +48 q^{-64} +55 q^{-66} -17 q^{-68} -64 q^{-70} -19 q^{-72} +21 q^{-74} +50 q^{-76} +10 q^{-78} -32 q^{-80} -19 q^{-82} -4 q^{-84} +22 q^{-86} +10 q^{-88} -7 q^{-90} -3 q^{-92} -6 q^{-94} +4 q^{-96} +2 q^{-98} -2 q^{-100} + q^{-102} -2 q^{-104} + q^{-106} - q^{-110} + q^{-112} }[/math] |
| 5 | [math]\displaystyle{ -q^{85}+q^{83}+2 q^{81}-q^{77}-3 q^{75}-4 q^{73}+8 q^{69}+8 q^{67}+2 q^{65}-7 q^{63}-16 q^{61}-14 q^{59}+4 q^{57}+26 q^{55}+29 q^{53}+10 q^{51}-23 q^{49}-49 q^{47}-39 q^{45}+7 q^{43}+59 q^{41}+71 q^{39}+31 q^{37}-43 q^{35}-97 q^{33}-82 q^{31}+2 q^{29}+98 q^{27}+127 q^{25}+61 q^{23}-66 q^{21}-153 q^{19}-129 q^{17}+2 q^{15}+149 q^{13}+181 q^{11}+66 q^9-107 q^7-208 q^5-143 q^3+53 q+209 q^{-1} +185 q^{-3} +16 q^{-5} -176 q^{-7} -215 q^{-9} -60 q^{-11} +146 q^{-13} +214 q^{-15} +94 q^{-17} -100 q^{-19} -198 q^{-21} -105 q^{-23} +78 q^{-25} +170 q^{-27} +104 q^{-29} -55 q^{-31} -147 q^{-33} -93 q^{-35} +40 q^{-37} +124 q^{-39} +82 q^{-41} -32 q^{-43} -108 q^{-45} -81 q^{-47} +14 q^{-49} +92 q^{-51} +84 q^{-53} +12 q^{-55} -69 q^{-57} -102 q^{-59} -55 q^{-61} +46 q^{-63} +112 q^{-65} +105 q^{-67} +9 q^{-69} -122 q^{-71} -164 q^{-73} -60 q^{-75} +104 q^{-77} +204 q^{-79} +139 q^{-81} -71 q^{-83} -236 q^{-85} -193 q^{-87} +11 q^{-89} +218 q^{-91} +241 q^{-93} +50 q^{-95} -176 q^{-97} -246 q^{-99} -100 q^{-101} +113 q^{-103} +213 q^{-105} +131 q^{-107} -46 q^{-109} -160 q^{-111} -128 q^{-113} + q^{-115} +98 q^{-117} +99 q^{-119} +27 q^{-121} -47 q^{-123} -64 q^{-125} -31 q^{-127} +17 q^{-129} +32 q^{-131} +20 q^{-133} - q^{-135} -13 q^{-137} -12 q^{-139} -4 q^{-141} +6 q^{-143} +5 q^{-145} - q^{-151} -2 q^{-153} + q^{-155} +2 q^{-157} - q^{-159} + q^{-163} - q^{-165} }[/math] |
A2 Invariants.
| Weight | Invariant |
|---|---|
| 1,0 | [math]\displaystyle{ -q^6-q^2+2 q^{-2} + q^{-4} +4 q^{-6} + q^{-8} + q^{-10} - q^{-12} -2 q^{-14} - q^{-18} }[/math] |
| 1,1 | [math]\displaystyle{ q^{20}-2 q^{18}+6 q^{16}-12 q^{14}+19 q^{12}-28 q^{10}+36 q^8-44 q^6+39 q^4-40 q^2+26-10 q^{-2} -8 q^{-4} +34 q^{-6} -40 q^{-8} +70 q^{-10} -67 q^{-12} +80 q^{-14} -70 q^{-16} +60 q^{-18} -49 q^{-20} +24 q^{-22} -12 q^{-24} -12 q^{-26} +23 q^{-28} -34 q^{-30} +34 q^{-32} -34 q^{-34} +32 q^{-36} -26 q^{-38} +18 q^{-40} -14 q^{-42} +11 q^{-44} -6 q^{-46} +4 q^{-48} -2 q^{-50} + q^{-52} }[/math] |
| 2,0 | [math]\displaystyle{ q^{18}-q^{14}+q^{10}-q^8-3 q^6-q^4+q^2-2-2 q^{-2} +3 q^{-4} + q^{-6} + q^{-8} +3 q^{-10} +6 q^{-12} +4 q^{-14} +5 q^{-16} +6 q^{-18} +2 q^{-20} -4 q^{-22} -3 q^{-24} -3 q^{-26} -7 q^{-28} -4 q^{-30} - q^{-36} +2 q^{-40} + q^{-42} + q^{-46} }[/math] |
| 3,0 | [math]\displaystyle{ -q^{36}+q^{32}+2 q^{30}-3 q^{26}-q^{24}+3 q^{22}+6 q^{20}-7 q^{16}-6 q^{14}+3 q^{12}+8 q^{10}-12 q^6-9 q^4+3 q^2+10- q^{-2} -9 q^{-4} -3 q^{-6} +8 q^{-8} +10 q^{-10} - q^{-12} -2 q^{-14} +3 q^{-16} +10 q^{-18} +4 q^{-20} +4 q^{-24} +11 q^{-26} +5 q^{-28} + q^{-30} +9 q^{-34} +4 q^{-36} -11 q^{-38} -18 q^{-40} -9 q^{-42} +3 q^{-44} -4 q^{-46} -13 q^{-48} -14 q^{-50} +4 q^{-52} +10 q^{-54} +4 q^{-56} -5 q^{-58} -4 q^{-60} +7 q^{-62} +10 q^{-64} +4 q^{-66} - q^{-68} -2 q^{-70} +2 q^{-72} + q^{-74} - q^{-76} - q^{-78} - q^{-80} - q^{-84} }[/math] |
A3 Invariants.
| Weight | Invariant |
|---|---|
| 0,1,0 | [math]\displaystyle{ q^{14}-q^{12}+q^{10}+q^8-4 q^6-2 q^2-7+ q^{-2} +3 q^{-4} +9 q^{-8} +10 q^{-10} +6 q^{-12} +3 q^{-14} + q^{-16} -2 q^{-18} -6 q^{-20} -6 q^{-22} + q^{-24} -4 q^{-26} -3 q^{-28} +5 q^{-30} -2 q^{-32} -2 q^{-34} +3 q^{-36} - q^{-40} + q^{-42} }[/math] |
| 1,0,0 | [math]\displaystyle{ -q^7-2 q^3- q^{-1} +2 q^{-3} +2 q^{-5} +4 q^{-7} +4 q^{-9} +2 q^{-11} + q^{-13} -2 q^{-15} - q^{-17} -3 q^{-19} - q^{-23} }[/math] |
| 1,0,1 | [math]\displaystyle{ q^{24}-2 q^{22}+5 q^{20}-5 q^{18}+2 q^{16}+6 q^{14}-16 q^{12}+24 q^{10}-21 q^8+7 q^6+7 q^4-39 q^2+35-47 q^{-2} +14 q^{-4} +4 q^{-6} -21 q^{-8} +47 q^{-10} -7 q^{-12} +34 q^{-14} +21 q^{-16} +16 q^{-18} +19 q^{-22} -26 q^{-24} -13 q^{-26} +7 q^{-28} -54 q^{-30} +29 q^{-32} -29 q^{-34} -2 q^{-36} +27 q^{-38} -32 q^{-40} +31 q^{-42} -7 q^{-44} -10 q^{-46} +21 q^{-48} -19 q^{-50} +5 q^{-52} +5 q^{-54} -9 q^{-56} +9 q^{-58} -3 q^{-60} - q^{-62} +3 q^{-64} -2 q^{-66} + q^{-68} }[/math] |
A4 Invariants.
| Weight | Invariant |
|---|---|
| 0,1,0,0 | [math]\displaystyle{ q^{16}+q^{12}+2 q^{10}-2 q^6-q^4-6 q^2-10-7 q^{-2} -4 q^{-4} -3 q^{-6} + q^{-8} +14 q^{-10} +17 q^{-12} +15 q^{-14} +16 q^{-16} +17 q^{-18} +2 q^{-20} -3 q^{-22} -4 q^{-24} -11 q^{-26} -14 q^{-28} -8 q^{-30} -4 q^{-32} -6 q^{-34} -2 q^{-36} +3 q^{-38} +2 q^{-40} -2 q^{-42} +2 q^{-44} +3 q^{-46} + q^{-52} }[/math] |
| 1,0,0,0 | [math]\displaystyle{ -q^8-2 q^4-q^2-1- q^{-2} +2 q^{-4} +2 q^{-6} +5 q^{-8} +4 q^{-10} +5 q^{-12} +2 q^{-14} + q^{-16} -2 q^{-18} -2 q^{-20} -2 q^{-22} -3 q^{-24} - q^{-28} }[/math] |
B2 Invariants.
| Weight | Invariant |
|---|---|
| 0,1 | [math]\displaystyle{ -q^{14}+q^{12}-3 q^{10}+3 q^8-4 q^6+4 q^4-4 q^2+3- q^{-2} + q^{-4} +4 q^{-6} -3 q^{-8} +8 q^{-10} -6 q^{-12} +9 q^{-14} -7 q^{-16} +6 q^{-18} -4 q^{-20} +2 q^{-22} - q^{-24} -2 q^{-26} +3 q^{-28} -5 q^{-30} +4 q^{-32} -4 q^{-34} +3 q^{-36} -2 q^{-38} + q^{-40} - q^{-42} }[/math] |
| 1,0 | [math]\displaystyle{ q^{24}-q^{20}-q^{18}+2 q^{16}+2 q^{14}-2 q^{12}-4 q^{10}-q^8+3 q^6+q^4-5 q^2-5+ q^{-2} +4 q^{-4} +2 q^{-6} -3 q^{-8} + q^{-10} +5 q^{-12} +6 q^{-14} + q^{-16} +2 q^{-18} +4 q^{-20} +5 q^{-22} -3 q^{-26} - q^{-28} +2 q^{-30} - q^{-32} -5 q^{-34} -4 q^{-36} + q^{-38} +2 q^{-40} -3 q^{-42} -5 q^{-44} +5 q^{-48} + q^{-50} -3 q^{-52} -3 q^{-54} + q^{-56} +3 q^{-58} + q^{-60} - q^{-62} - q^{-64} + q^{-68} }[/math] |
D4 Invariants.
| Weight | Invariant |
|---|---|
| 1,0,0,0 | [math]\displaystyle{ q^{18}-q^{16}+2 q^{14}-2 q^{12}+3 q^{10}-4 q^8+q^6-6 q^4-6-2 q^{-2} -2 q^{-4} + q^{-6} +5 q^{-8} +3 q^{-10} +13 q^{-12} +5 q^{-14} +14 q^{-16} +9 q^{-20} -5 q^{-22} +3 q^{-24} -9 q^{-26} -3 q^{-28} -7 q^{-30} -2 q^{-32} -2 q^{-34} -3 q^{-36} + q^{-38} -3 q^{-40} +5 q^{-42} -3 q^{-44} +2 q^{-46} -3 q^{-48} +3 q^{-50} - q^{-52} + q^{-54} - q^{-56} + q^{-58} }[/math] |
G2 Invariants.
| Weight | Invariant |
|---|---|
| 1,0 | [math]\displaystyle{ q^{32}-q^{30}+3 q^{28}-4 q^{26}+2 q^{24}-q^{22}-5 q^{20}+9 q^{18}-12 q^{16}+10 q^{14}-6 q^{12}-5 q^{10}+12 q^8-16 q^6+14 q^4-9 q^2-2+9 q^{-2} -13 q^{-4} +9 q^{-6} - q^{-8} -4 q^{-10} +12 q^{-12} -7 q^{-14} +3 q^{-16} +7 q^{-18} -10 q^{-20} +19 q^{-22} -14 q^{-24} +9 q^{-26} +7 q^{-28} -12 q^{-30} +23 q^{-32} -19 q^{-34} +14 q^{-36} - q^{-38} -7 q^{-40} +13 q^{-42} -17 q^{-44} +11 q^{-46} - q^{-48} -7 q^{-50} +8 q^{-52} -8 q^{-54} -2 q^{-56} +8 q^{-58} -14 q^{-60} +9 q^{-62} -6 q^{-64} -3 q^{-66} +9 q^{-68} -14 q^{-70} +14 q^{-72} -8 q^{-74} +2 q^{-76} +2 q^{-78} -7 q^{-80} +6 q^{-82} -6 q^{-84} +5 q^{-86} -2 q^{-88} + q^{-92} -2 q^{-94} +2 q^{-96} - q^{-98} + q^{-100} }[/math] |
