$\DeclareMathOperator\SL{SL}\DeclareMathOperator\GL{GL}$Let $K$ be a field of characteristic zero, and let $\overline{K}$ be an algebraic closure of $K$. Is it true that the irreducible, projective, rational representations $$ \SL_n(K) \rightarrow \GL_m(\overline{K}) $$ are just restriction to $\SL_n(K)$ of the Weyl modules plus field automorphisms? References and comments are most appreciative. Thanks!

Note: Rational representation == given by rational map of algebraic varieties.