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-2/3 | 0 | 1 | 2 | 4 | 6 | 8 | |
\mathbbR | 0 | 0 | A1 | A2 | C3 | C3.H14 | F4 |
\mathbbC | 0 | T2 | A2 | 2A2 | A5 | A5.H20 | E6 |
\mathbbH | A1 | 3A1 | C3 | A5 | D6 | D6.H32 | E7 |
\mathbbS | A1.H4 | (3A1).H8 | C3.H14 | A5.H20 | D6.H32 | D6.H32.H44 | E7.H56 |
\mathbbO | G2 | D4 | F4 | E6 | E7 | E7.H56 | E8 |
m | -2 | -2/3 | 0 | 1 | 2 | 4 | 6 | 8 |
G | A2 | 0 | T2 | A2 | A2ÅA2 | A5 | A5.H20 | E6 |
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A2 | A2 | 2A2 | A5 | E6 | |
V | -[1,0] | [2,0] | [0,1|1,0] | [0,1,0,0,0] | [1,0,0,0,0,0] |
\mathfrakg | [1,1] | [1,1] | [1,1|0,0] | [1,0,0,0,1] | [0,1,0,0,0,0] |
V2 | -[2,0] | [2,1] | [1,0|2,0] | [1,0,1,0,0] | [0,0,1,0,0,0] |
0 | 1 | 2 | |
\mathfrakg | l1+l5 | l3 | 1 |
V | l2 | l5 | |
V* | l4 | l1 | |
V2 | 2l2 | (l2+l5) | l5 |
V2 | (l1+l3) | (l2+l5)Ål1 | l4 |
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Vp | 4p2/3 + 2pm |
V2Vp | 4p2/3 + 2p(3m+5)/3 + 4(3m+1)/3 |
V*Vp | 4p2/3 + 2p(3m+2)/3 + 2(3m+2)/3 |
\mathfrakgVp | 4p2/3 + 2p(m+1) + 3m |
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m | -2/3 | 0 | 1 | 2 | 4 | 6 | 8 |
G | A1 | 3A1 | C3 | A5 | D6 | D6.H32 | E7 |
m | -3 | -8/3 | -5/2 | -2 | -4/3 | -1 |
G | D5 | B3 | G2 | 2A1 | 0 | D(2,1,a) |
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A1 | 3A1 | C3 | A5 | D6 | E7 | |
V | [3] | [1,1,1] | [0,0,1] | [0,0,1,0,0] | [0,0,0,0,0,1] | [0,0,0,0,0,0,1] |
V2 | [4] | [2,2,0] | [0,2,0] | [0,1,0,1,0] | [0,0,0,1,0,0] | [0,0,0,0,0,1,0] |
0 | 1 | 2 | |
\mathfrakg | l2 | l5 | 1 |
V | l6 | l1 | |
V2 | 2l6 | (l1+l6) | 2l1 |
V2 | l4 | (l1+l6) | l2 |
D5 | B3 | G2 | 2A1 | |
V | -[1,0,0,0,0] | -[0,0,1] | -[1,0] | -[1]Ä[1] |
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Vp | 3p2/4 + p(3m+3)/2 |
\mathfrakgVp | 3p2/4 + p(3m+5)/2 + 2m + 2 |
V2Vp | 3p2/4 + p(3m+7) + 3m + 4 |
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m | -5/2 | -3/2 | -4/3 | -1 | -2/3 | 0 | 1 | 2 | 4 | 6 | 8 |
G | 1 | SOSp(2,1) | A1 | A2 | G2 | D4 | F4 | E6 | E7 | E7.H56 | E8 |
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G | \mathfrakg | X | Y(a) | Y(b) | Y(g) |
\spl (n) | l1+ln | l2+2ln | 2l1+2l2 | l1+ln | l2+ln-1 |
\so (n) | l2 | l1+l3 | 2l2 | l4 | 2l2 |
\syp (2n) | 2l1 | 2l1+l2 | 2l2 | 4l1 | l2 |
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a | b | g | ||
\spl (n) | -2 | 2 | n | a+b = 0 |
\so (n) | -2 | 4 | n-2 | 2a+b = 0 |
\syp (2n) | -2 | 4 | -2n-2 | 2a+b = 0 |
\mathbbO | -2 | m+4 | 2m+4 | 2a+2b-g = 0 |
\mathbbH | -2 | m | m+4 | 2a-b+g = 0 |
0 | 1 | 2 | 3 | 4 | |
\mathfrakg | 2l1 | l1 | 1 | ||
X | (2l1+l2) | (l1+l2)Å3l1 | l2Å2l1 | l1 | |
Y(a) | 2l2 | (l1+l2) | 2l1 | l-1 | 1 |
Y(b) | 4l1 | 3l1 | |||
Y(g) | l2 | l1 |
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0 | 1 | 2 | 3 | 4 | dim | |
\mathfrakg | l1 | l7 | 1 | 190 | ||
X | l3 | (l1+l7)Ål2 | l1Ål6 | l7 | 17765 | |
\mathfrakg2 | 2l1 | (l1+l7) | l1Å2l7 | l7 | 1 | 15504 |
Y | l6 | l2Ål7 | l1 | 2640 |
0 | 1 | 2 | 3 | 4 | dim | |
\mathfrakg | l2 | l5 | 1 | 99 | ||
X | (l1+l3) | (l2+l5)Å(l1+l6) | l2Ål4 | l5 | 4752 | |
Y(a) | 2l2 | (l1+l5) | l2Å2l5 | l5 | 1 | 3927 |
Y(b) | l4 | l5Å(l1+l6) | l2 | 945 | ||
Y(g) | 2l1 | 77 |
0 | 1 | 2 |
78 | 64+13 | 1 |
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m | -2/3 | 0 | 1 | 2 | 4 | 6 | 8 |
G | 0 | 0 | A1 | A2 | C3 | C3.H14 | F4 |
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A1 | A2 | C3 | F4 | |
V | [4] | [1,1] | [0,1,0] | [0,0,0,1] |
\mathfrakg | [2] | [1,1] | [2,0,0] | [1,0,0,0] |
V2 | [6] | [3,0] | [1,0,1] | [0,0,1,0] |
0 | 1 | 2 | |
\mathfrakg | 2l1 | l3 | 1 |
V | l2 | l1 | |
V2 | 2l2 | (l1+l2) | l3 |
V2 | l1+l3 | l1Å(l1+l2) | l2 |
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