Affine groups of flat surfaces
Affine groups of flat surfaces
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DOI：
10.4171/055
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发表时间：
2005-11
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影响因子：
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通讯作者：
Sean Lawton;Elisha Peterson
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文献类型：
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作者：
Sean Lawton;Elisha Peterson
用F_2表示2个字母上的自由群，用R=Hom(F_2，SL(2，C))表示F_2的SL(2，C)表示簇。基团SL(2，C)通过共轭作用于R。我们构造了坐标环C[SL(2，C)]与矩阵系数环之间的同构，从而提供了C[R]^SL(2，C)关于自旋网络的加法基。利用图解演算，我们确定了这个基的对称性和乘法结构。给出了F_2的SL(2，C)特征标簇上正则函数的典范刻画，并对Fricke，Klein和Vogt的一个经典结果给出了新的证明。
Denote the free group on 2 letters by F_2 and the SL(2,C)-representation variety of F_2 by R=Hom(F_2,SL(2,C)). The group SL(2,C) acts on R by conjugation. We construct an isomorphism between the coordinate ring C[SL(2,C)] and the ring of matrix coefficients, providing an additive basis of C[R]^SL(2,C) in terms of spin networks. Using a graphical calculus, we determine the symmetries and multiplicative structure of this basis. This gives a canonical description of the regular functions on the SL(2,C)-character variety of F_2 and a new proof of a classical result of Fricke, Klein, and Vogt.