■可積分系とテータ関数(その21)

 格子のボロノイ細胞V(0)に対する慣性モーメントの計算結果を示したい.

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[1]An型格子

  I(V(0))=I(S)=n/12+n/6(n+1)

  G(An)=1/n・I(V(0))/vol(V(0))^(2/n)

=1/(n+1)^1/n・{n/12+n/6(n+1)}

→1/12

−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

[2]Dn型格子

  G(Dn)=1/2^2/n・{1/12+1/2n(n+1)}

→1/12

−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

[3]E型格子

  G(E8)=929/12960=0.0716821

  G(E7)=163/2016・2^-1/7=0.0732306

  G(E6)=5/56・3^-1/6=0.0743467

−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

[4]E*型格子

  G(E6*)=12619・3^1/6/204120=0.0742437

  G(E7*)=21361・2^1/7/322560=0.0731165

−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

[5]D*型格子

  G(D3*)=19/192・2^1/3

  G(D4*)=13/120√2

  G(D5*)=2641/23040・2^3/5=0.0756254

  G(D6*)=601・2^1/3/10080=0.0751203

−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

[6]A*型格子

  G(An*)=Jn+1/n(n+1)^(1-1/n)

  J1=0,J2=1/12,J3=5/18,J4=19/32

  J5=389/375,J6=1045/648,J7=78077/33614

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