Indeed,I'm reading the book《representation theory and complex geometry》,there is a proof of the fact that Pic(G)is trivial when G is a simple-connected semisimple algebraic group over C,but the proof is not self-contained,it use some results from representation theory in BGG's article《schubert cells and cohomology of the space G/P. So I'm wondering whether there are other ways to show this fact. And whether the assertion still holds ture when we change the base field C. thanks for all the comments