| Résume | McShane established a remarkable identity for the lengths of simple closed geodesics on the hyperbolic surface with cusps. Mirzakhani extended McShane identity to obtain a beautiful recursive formula for the volumes of the moduli spaces of the Riemann surfaces, which again proved the Witten-Kontsevich theorem. On the other hand, Goncharov and Shen formulated an explicit homological mirror symmetry on two variations of moduli spaces of G-local systems using the so-called Goncharov-Shen potential. Using these Goncharov-Shen potentials, we found a collection of new McShane-type
identities parametrized by the pairs (cusp/hole, simple positive root), which are the analogs of McShane-Mirzakhani identities with new parameters in the case of higher rank Lie groups, which provided us some expectations to generalize Mirzakhani's recursive formula to the higher rank cases |
