■リー群と表現(その84)
【1】E7無限鏡映群の基本単体の頂点座標
(0,0,0,0,0,0,0,0)
(0,0,0,0,0,0,1/2,−1/2)
(1/6,−1/6,−1/6,−1/6,−1/6,−1/6,1/2,−1/2)
(0,0,−1/4,−1/4,−1/4,−1/4,1/2,−1/2)
(0,0,0,−1/3,−1/3,−1/3,1/2,−1/2)
(0,0,0,0,−1/2,−1/2,1/2,−1/2)
(0,0,0,0,0,−1,1/2,−1/2)
(−1/4,−1/4,−1/4,−1/4,−1/4,−1/4,1/2,−1/2)
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【2】E7のボロノイ細胞
[1]x7−x8=1
[2]x1+x8=x2+x3+・・・+x7
[3]x1=x2
[4]x2=x3
[5]x3=x4
[6]x4=x5
[7]x5=x6
[8]x1=−x2
[2]を外すと
x1=x2=x3=x4=x5=x6=0
x7=1/2,x8=−1/2
[3]を外すと
x1=1/6
x2=x3=x4=x5=x6=−1/6
x7=1/2,x8=−1/2
[4]を外すと
x1=x2=0
x3=x4=x5=x6=−1/4
x7=1/2,x8=−1/2
[5]を外すと
x1=x2=x3=0
x4=x5=x6=−1/3
x7=1/2,x8=−1/2
[6]を外すと
x1=x2=x3=x4=0
x5=x6=−1/2
x7=1/2,x8=−1/2
[7]を外すと
x1=x2=x3=x4=x5=0
x6=−1
x7=1/2,x8=−1/2
[8]を外すと
x1=x2=x3=x4=x5=x6=1/4
x7=1/2,x8=−1/2
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【3】E7~について(331)
(0,0,0,0,0,0,0)
(1,0,0,0,0,0,0)
(1,1/√3,0,0,0,0,0)
(1,1/√3,1/√6,0,0,0,0)
(1,1/√3,1/√6,1/√6,0,0,0)
(1,1/√3,1/√6,1/√6,1/√3,0,0)
(1,1/√3,1/√6,1/√6,1/√3,1,0)
(1,1/√3,1/√6,0,0,0,1/2)
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