Fock–Goncharov coordinates for semisimple Lie groups
Fock–Goncharov coordinates for semisimple Lie groups
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Date
2021
Authors
Gilles, S
Advisor
Zickert, Christian
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Abstract
Fock and Goncharov introduced cluster ensembles, providing a framework for coordinates on varieties of
surface representations into Lie groups, as well as a complete
construction for groups of type $A_n$. Later, Zickert,
Le , and Ip
described, using differing methods, how to apply this
framework for other Lie group types. Zickert also showed that this
framework applies to triangulated $3$-manifolds. We present a
complete, general construction, based on work of Fomin and
Zelevinsky. In particular, we complete the picture for the remaining
cases: Lie groups of types $F_4$, $E_6$, $E_7$, and $E_8$.