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Some aspects of Aomoto's generalized hypergeometric functions on Grassmannianspaces $Gr(k+1,n+1)$ are reviewed. Particularly, their integral representationsin terms of twisted homology and cohomology are clarified with an example ofthe $Gr(2,4)$ case which corresponds to Gauss' hypergeometric functions. Thecases of $Gr(2, n+1)$ in general lead to $(n+1)$-point solutions of theKnizhnik-Zamolodchikov (KZ) equation. We further analyze theSchechtman-Varchenko integral representations of the KZ solutions in relationto the $Gr(k+1, n+1)$ cases. We show that holonomy operators of the so-calledKZ connections can be interpreted as hypergeometric-type integrals. This resultleads to an improved description of a recently proposed holonomy formalism forgluon amplitudes. We also present a (co)homology interpretation of Grassmannianformulations for scattering amplitudes in ${\cal N} = 4$ super Yang-Millstheory.

A note on generalized hypergeometric functions, KZ solutions, and gluon amplitudes