Let $G$ be a simple complex algebraic group. What are its complex irreducible finite-dimensional representations?

Before you start voting to close the question, I never said "rational". I am asking about abstract representations of $G$ as a group.

I can a make an obvious conjecture but I have no idea how to prove it, even for $SL_2$. Yet, it could be something well-known. Pick a rational irreducible representation $(V,\rho)$ and a field endomorphism $\tau: {\mathbb C} \rightarrow {\mathbb C}$. The field endomorphism extends to an endmorphism of $G$: just apply $\tau$ to each matrix entry of of $g\in G\subseteq GL_n(\mathbb C)$. Thus, we get a twisted rational representation $(V,\tau\circ \rho)$ that clearly remains irreducible.

STUPID WABBIT CONJECTURE: all irreducible representations are twisted rational representations.