Given a reductive algebraic group $G$ and a maximal torus $T$. Is it true that the functors $$ Hom_T(-,\lambda) $$ are exact, where $\lambda$ denotes one of the the simple one-dimensional representations of $T$? Why is this so? I feel this should be very elementary, but I can't seem to figure it out.
2026-03-30 11:57:19.1774871839
Exactness of Hom functor for torus representations?
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