1-cohomology of Chevalley groups (Q1262953)

Let G be a Chevalley group over the finite field \({\mathbb{F}}_ q\) and let B denote a Borel subgroup. The author considers extensions between the trivial module and simple modules. If the highest weight \(\lambda\) of the simple module is a fundamental weight he proves that except for a few cases where \(q\leq 3\) any such extension is realized as a quotient of the G-module induced from the B-module \(\lambda\). He also establishes the same result for general \(\lambda\) in many cases - including all cases where q is not a prime.