For Kähler groups with exact Kähler form, homogeneous projective special Kähler structures are equivalent to left-invariant matrix one-forms satisfying explicit algebraic-differential equations, and their c-map images are always homogeneous quaternionic Kähler groups.
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The c-map on groups
For Kähler groups with exact Kähler form, homogeneous projective special Kähler structures are equivalent to left-invariant matrix one-forms satisfying explicit algebraic-differential equations, and their c-map images are always homogeneous quaternionic Kähler groups.