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Could you hint (or give a reference) for: A holomorphic group homomorphism between complex reductive algebraic groups is algebraic.

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    $\begingroup$ It suffices to treat the connected case, which is Proposition D.2.1 in the article Reductive Group Schemes in smf4.emath.fr/Publications/PanoramasSyntheses/2014/42-43/html/… (briefly: reduce to target ${\rm{GL}}_n$ and the source either a torus or semisimple, and for tori use the maximal compact subgroup and Lie algebra considerations whereas for semisimple source use a graph argument with semisimple Lie algebras). $\endgroup$
    – nfdc23
    Commented Dec 15, 2017 at 1:09

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