Let G be a semisimple, simply connected algebraic group over a field k, and let B be a Borel subgroup. The motivation of this paper is the study of tensor products of G-modules. For a dominant weight \(\lambda\), let L(\(\lambda\)) denote the associated Weyl module. The Bruhat decomposition of G/B\(\times G/B\) (for the diagonal action of G) induces a filtration on L(\(\lambda\))\(\otimes L(\mu).\) Problem: Does the G-module L(\(\lambda\))\(\otimes L(\mu)\) have a filtration whose subquotients are Weyl modules, and which is compatible with the filtration induced by the Bruhat decomposition. The above problem has been answered in the affirmative either if the characteristic of k is large or G does not contain a factor of type \(E_ 7\) or \(E_ 8\), by Donkin, Polo, Wang etc. some of these proofs being case by case analysis. The methods in this paper provide a general proof to some cases of the above problem. In addition, the author also proves some auxiliary results on filtrations of B-modules. This paper makes a nice contribution to the representation theory of algebraic groups.