10 132 Quantum Invariants
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A1 Invariants.
Weight
Invariant
1
−
q
15
+
q
7
+
q
5
+
q
3
{\displaystyle -q^{15}+q^{7}+q^{5}+q^{3}}
2
q
44
−
q
40
−
q
30
−
q
24
+
q
16
+
q
14
+
q
10
+
q
6
+
2
−
q
−
4
{\displaystyle q^{44}-q^{40}-q^{30}-q^{24}+q^{16}+q^{14}+q^{10}+q^{6}+2-q^{-4}}
3
−
q
87
+
q
83
+
q
81
−
q
77
+
q
67
−
q
63
+
q
59
+
q
57
−
q
55
−
q
53
−
q
45
−
q
43
+
q
39
−
q
35
+
q
31
−
q
27
−
q
25
+
q
17
+
2
q
15
+
2
q
13
+
q
7
+
2
q
5
+
q
3
−
q
−
q
−
1
{\displaystyle -q^{87}+q^{83}+q^{81}-q^{77}+q^{67}-q^{63}+q^{59}+q^{57}-q^{55}-q^{53}-q^{45}-q^{43}+q^{39}-q^{35}+q^{31}-q^{27}-q^{25}+q^{17}+2q^{15}+2q^{13}+q^{7}+2q^{5}+q^{3}-q-q^{-1}}
A2 Invariants.
Weight
Invariant
1,0
−
q
22
−
q
20
−
q
18
+
q
14
+
q
12
+
2
q
10
+
q
8
+
q
6
{\displaystyle -q^{22}-q^{20}-q^{18}+q^{14}+q^{12}+2q^{10}+q^{8}+q^{6}}
1,1
q
60
+
2
q
56
−
2
q
50
−
2
q
48
−
2
q
44
+
2
q
36
−
2
q
34
−
2
q
30
−
q
28
−
2
q
24
+
2
q
22
−
q
20
+
4
q
18
+
6
q
14
+
q
12
+
4
q
10
+
2
q
8
−
2
q
6
+
2
q
4
−
2
q
2
+
2
−
2
q
−
2
{\displaystyle q^{60}+2q^{56}-2q^{50}-2q^{48}-2q^{44}+2q^{36}-2q^{34}-2q^{30}-q^{28}-2q^{24}+2q^{22}-q^{20}+4q^{18}+6q^{14}+q^{12}+4q^{10}+2q^{8}-2q^{6}+2q^{4}-2q^{2}+2-2q^{-2}}
2,0
q
58
+
q
56
+
q
54
−
q
48
−
q
46
−
2
q
44
−
2
q
42
−
2
q
40
−
q
38
+
q
36
−
q
34
+
q
28
+
q
24
+
2
q
22
+
2
q
20
+
q
18
+
q
16
+
q
14
+
q
10
+
q
8
+
q
4
+
q
2
+
1
−
q
−
2
−
q
−
4
{\displaystyle q^{58}+q^{56}+q^{54}-q^{48}-q^{46}-2q^{44}-2q^{42}-2q^{40}-q^{38}+q^{36}-q^{34}+q^{28}+q^{24}+2q^{22}+2q^{20}+q^{18}+q^{16}+q^{14}+q^{10}+q^{8}+q^{4}+q^{2}+1-q^{-2}-q^{-4}}
A3 Invariants.
Weight
Invariant
0,1,0
q
46
+
q
42
+
q
40
−
2
q
36
−
2
q
34
−
4
q
32
−
5
q
30
−
2
q
28
−
q
26
+
2
q
24
+
3
q
22
+
6
q
20
+
4
q
18
+
3
q
16
+
2
q
14
+
q
12
−
q
10
−
q
8
−
q
4
+
1
{\displaystyle q^{46}+q^{42}+q^{40}-2q^{36}-2q^{34}-4q^{32}-5q^{30}-2q^{28}-q^{26}+2q^{24}+3q^{22}+6q^{20}+4q^{18}+3q^{16}+2q^{14}+q^{12}-q^{10}-q^{8}-q^{4}+1}
1,0,0
−
q
29
−
q
27
−
2
q
25
−
q
23
+
q
19
+
2
q
17
+
2
q
15
+
2
q
13
+
q
11
+
q
9
{\displaystyle -q^{29}-q^{27}-2q^{25}-q^{23}+q^{19}+2q^{17}+2q^{15}+2q^{13}+q^{11}+q^{9}}
A4 Invariants.
Weight
Invariant
0,1,0,0
q
60
+
q
58
+
2
q
56
+
2
q
54
+
2
q
52
+
q
50
−
q
48
−
4
q
46
−
6
q
44
−
8
q
42
−
9
q
40
−
8
q
38
−
5
q
36
+
4
q
32
+
8
q
30
+
11
q
28
+
11
q
26
+
8
q
24
+
6
q
22
+
q
20
−
q
18
−
3
q
16
−
2
q
14
−
2
q
12
−
q
10
+
q
6
+
1
{\displaystyle q^{60}+q^{58}+2q^{56}+2q^{54}+2q^{52}+q^{50}-q^{48}-4q^{46}-6q^{44}-8q^{42}-9q^{40}-8q^{38}-5q^{36}+4q^{32}+8q^{30}+11q^{28}+11q^{26}+8q^{24}+6q^{22}+q^{20}-q^{18}-3q^{16}-2q^{14}-2q^{12}-q^{10}+q^{6}+1}
1,0,0,0
−
q
36
−
q
34
−
2
q
32
−
2
q
30
−
q
28
+
q
24
+
2
q
22
+
3
q
20
+
2
q
18
+
2
q
16
+
q
14
+
q
12
{\displaystyle -q^{36}-q^{34}-2q^{32}-2q^{30}-q^{28}+q^{24}+2q^{22}+3q^{20}+2q^{18}+2q^{16}+q^{14}+q^{12}}
B2 Invariants.
Weight
Invariant
0,1
−
q
46
−
q
42
−
q
40
+
q
30
+
q
26
+
q
22
+
q
16
+
q
12
+
q
10
+
q
8
+
q
4
−
1
{\displaystyle -q^{46}-q^{42}-q^{40}+q^{30}+q^{26}+q^{22}+q^{16}+q^{12}+q^{10}+q^{8}+q^{4}-1}
1,0
q
76
+
q
68
−
q
58
−
2
q
56
−
q
54
−
q
52
−
2
q
50
−
2
q
48
−
q
46
−
q
44
+
q
38
+
q
36
+
2
q
34
+
2
q
32
+
2
q
30
+
q
28
+
2
q
26
+
2
q
24
+
q
22
+
q
18
−
q
12
−
q
4
+
1
{\displaystyle q^{76}+q^{68}-q^{58}-2q^{56}-q^{54}-q^{52}-2q^{50}-2q^{48}-q^{46}-q^{44}+q^{38}+q^{36}+2q^{34}+2q^{32}+2q^{30}+q^{28}+2q^{26}+2q^{24}+q^{22}+q^{18}-q^{12}-q^{4}+1}
G2 Invariants.
Weight
Invariant
1,0
q
108
+
q
104
−
q
100
−
q
92
−
q
90
−
q
86
−
q
84
−
q
82
−
2
q
80
−
q
78
−
q
76
−
2
q
74
−
q
68
−
q
64
+
q
62
+
q
60
+
q
58
+
q
56
+
q
54
+
2
q
52
+
3
q
50
+
q
48
+
q
46
+
2
q
44
+
q
42
+
2
q
40
+
q
38
+
q
34
+
q
32
−
q
28
+
q
26
−
q
24
−
q
18
+
q
16
−
q
12
+
q
4
−
q
2
+
1
+
q
−
6
−
q
−
8
{\displaystyle q^{108}+q^{104}-q^{100}-q^{92}-q^{90}-q^{86}-q^{84}-q^{82}-2q^{80}-q^{78}-q^{76}-2q^{74}-q^{68}-q^{64}+q^{62}+q^{60}+q^{58}+q^{56}+q^{54}+2q^{52}+3q^{50}+q^{48}+q^{46}+2q^{44}+q^{42}+2q^{40}+q^{38}+q^{34}+q^{32}-q^{28}+q^{26}-q^{24}-q^{18}+q^{16}-q^{12}+q^{4}-q^{2}+1+q^{-6}-q^{-8}}
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