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See detailTropical Fock-Goncharov coordinates for SL3-webs on surfaces II: naturality
Sun, Zhe UL; Douglas, Daniel C.

E-print/Working paper (2020)

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See detailTropical Fock-Goncharov coordinates for SL3-webs on surfaces I: construction
Sun, Zhe UL; Douglas, Daniel C.

E-print/Working paper (2020)

For a finite-type surface S, we study a preferred basis for the commutative algebra C[XSL3(C)(S)] of regular functions on the SL3(C)-character variety, introduced by Sikora and Westbury. These basis ... [more ▼]

For a finite-type surface S, we study a preferred basis for the commutative algebra C[XSL3(C)(S)] of regular functions on the SL3(C)-character variety, introduced by Sikora and Westbury. These basis elements come from the trace functions associated to certain tri-valent graphs embedded in the surface S. We show that this basis can be naturally indexed by positive integer coordinates, defined by Knutson-Tao rhombus inequalities. These coordinates are related, by the geometric theory of Fock and Goncharov, to the tropical points at infinity of the dual version of the character variety. [less ▲]

Detailed reference viewed: 46 (0 UL)