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Oct 4 at 15:21 comment added Sergey Guminov @AntoineLabelle This seems to be sufficient, see Proposition 6.2.17 of Pramod Achar's book. It basically says that for a connected algebraic group $G$ acting on $X$ any isomorphism between the two pullbacks of a perverse sheaf on $X$ to $G\times X$ gives an equivariant structure.
Jul 13, 2023 at 3:20 comment added Antoine Labelle Is this a sufficient condition for equivariance, or only necessary?
Jul 12, 2023 at 22:09 history edited LSpice CC BY-SA 4.0
G -> $G$
Jul 12, 2023 at 21:05 history answered Justin Hilburn CC BY-SA 4.0