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- W4247703075 abstract "Denote the free group on 2 letters by F2 and the SL(2,ℂ)-representation variety of F2 by R = Hom(F2,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 F2 and a new proof of a classical result of Fricke, Klein, and Vogt." @default.
- W4247703075 created "2022-05-12" @default.
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- W4247703075 date "2009-03-25" @default.
- W4247703075 modified "2023-09-26" @default.
- W4247703075 title "Spin networks and SL(2,ℂ)-character varieties" @default.
- W4247703075 doi "https://doi.org/10.4171/055-1/17" @default.
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