■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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