A space of meromorphic connections for tt*-Toda equations is shown to be a real symplectic Lie groupoid, with the universal centralizer proven to be a holomorphic symplectic groupoid over the Steinberg cross section.
Balibanu,Steinberg slices and group-valued moment maps, Adv
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Geometry of the tt*-Toda equations I: universal centralizer and symplectic groupoids
A space of meromorphic connections for tt*-Toda equations is shown to be a real symplectic Lie groupoid, with the universal centralizer proven to be a holomorphic symplectic groupoid over the Steinberg cross section.