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Nov 5, 2022 at 18:54 comment added user473423 I guess it should follow from highest weight theory that all homomorphisms of algebraic groups $SL_n\to PGL_m$ are defined over $\mathbb Q$. (Since both groups are split.) Hence there is no Galois action to consider, only those Homs of algebraic groups.
Nov 5, 2022 at 17:45 history edited YCor CC BY-SA 4.0
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Nov 5, 2022 at 17:04 history asked W Sao CC BY-SA 4.0