TITLE: Checking if Algebraic Groups are simply connected
QUESTION [7 upvotes]: I have recently been thnking some about algebraic groups and reading parts of Humphreys book on them, and I was wondering if there is a general process to showing they are simply connected. In particular I was wondering over other fields than $\mathbb{C}$ but if the answer only works in $\mathbb{C}$ I will settle for that. 
One idea I had was that using Borel-Weil-Bott one could make a slick arguement for when the fundamental group is trivial. I would like to get away from the ad-hoc thinking process I am using.

REPLY [3 votes]: Please see https://mathoverflow.net/questions/19262/simply-connectedness-of-algebraic-group