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Algebra Dynkin Diagram
A (su(2) or sl(2) )1
so(4) = su(2) + su(2)
G 2
2B (so(5) )
2A (su(3) or sl(3) )
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21 3
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i+1i i+k-1 i+k
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I
II
III
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1 2 p-1 p q q-1 1
1 2 p-1
s-1
2
1
q-1
2
1
A)
B)
C)
D)
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E 6
E 7
E 8
(p=3)
(p=4)
(p=5)
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1 2 3 r-1 r
rA ~ SU(r+1)
E 63 4 5
6
1 2
1 2 3 4 5 6
7
E 7
1 2 3 4 5 6 7
8
E 8
1 2 3 4
4F
1 2
2G
1 2 r-3 r-2
r-1
rrD ~ SO(2r)
1 2 r-2 r-1 r
rC ~ Sp(r)
rB ~ SO(2r+1)
1 2 r-2 r-1 r
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+ + + + +
+ + +
+ + + + +
2
1
1
2
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2
1
22
1
11 1 2
1 1
1 2
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rB ~ SO(2r+1)
1 2 r-2 r-1 r
(2r+1)1 (2r+1) (2r+1) (2r+1)2 r-1 2
r
r-2
( )2r1
1 2 r-2 r-1 r
rC ~ Sp(r)
-( )2r ( )2r ]-( )2r ( )2r -( )2r ( )2rr-2 r-4 r-1 r-3 r r-2-( )2r ( )2r2 0[ ] [ ] [ [ ]
1 2 r-3 r-2
r-1
rrD ~ SO(2r)
( )2r
1
2r-1
2 r-1
( )2r
( )2r
( )2r
2 r-3 r-2
1 2 3 r-1 r
rA ~ SU(r+1)
( )r+1r-1( )1 ( ) ( ) ( )r+1 r+1 r+1 r+1
2 3 r
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78
27
351
2,925
351
27
(adjoint)
E6 912
133 (adjoint)
8,645
365,750
27,664
1,539
56
E7
147,250
3,875
6,696,000
87,587,590,464
5,121,384,450
24,502,400
72,912
248 (adjoint)
E8
26
273
1,274
52 (adjoint)
F4
714
(adjoint)
G2
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