An application of Guillemin–Abreu theory to a non-abelian group action

This note is a step towards demonstrating the benefits of a symplectic approach to studying equivariant Kähler geometry. We apply a local differential geometric framework from Kähler toric geometry due to Guillemin and Abreu to the case of the standard linear SU(n)SU(n) action on Cn∖{0}Cn∖{0}. Using this framework we (re)construct certain Kähler metrics from data on moment polytopes.