■リー群と表現(その85)
【1】E6無限鏡映群の基本単体の頂点座標
(0,0,0,0,0,0,0,0)
(1/4,1/4,1/4,1/4,1/4,−1/4,−1/4,1/4)
(0,0,1/3,1/3,1/3,−1/3,−1/3,1/3)
(0,0,0,1/2,1/2,−1/3,−1/3,1/3)
(0,0,0,0,1,−1/3,−1/3,1/3)
(−1/4,1/4,1/4,1/4,1/4,−5/12,−5/12,5/12)
(0,0,0,0,0,−2/3,−2/3,2/3)
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【2】E6のボロノイ細胞
[1]1/2(x1+x2+・・・+x8)=1
[2]x1+x8=x2+x3+・・・+x7
[3]x1=x2
[4]x2=x3
[5]x3=x4
[6]x4=x5
[7]x1=−x2
[2]を外すと
x1=x2=x3=x4=x5=0
x6=x7=−2/3
x8=2/3
[3]を外すと
x3=x4=x5=1/4
x1=−x2=−1/4
x6=x7=−5/12
x8=5/12
[4]を外すと
x4=x5=1/3
x1=x2=0
x6=x7=−1/3
x3=x8=1/3
[5]を外すと
x5=1/2
x1=x2=x3=0
x6=x7=−1/3
x3=0,x8=1/3
[6]を外すと
x1=x2=x3=x4=0
x6=x7=−1/3
x5=1,x8=1/3
[7]を外すと
x1=x2=x3=x4=x5=1/4
x6=x7=−1/4
x8=1/4
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【3】E6~について(222)
P0(0,0,0,0,0,0)
P1(1,0,0,0,0,0)
P2(1,1/√3,0,0,0,0)
P3(1,1/√3,1/√3,0,0,0)
P4(1,1/√3,1/√3,1,0,0)
P5(1,1/√3,0,0,1/√3,0)
P6(1,1/√3,0,0,1/√3,1)
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