■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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