On the good filtration dimension of Weyl modules for a linear algebraic group

Let G be a linear algebraic group over an algebraically closed field of characteristic p whose corresponding root system is irreducible. In this paper we calculate the Weyl filtration dimension of the induced G-modules, del(lambda) and the simple G-modules L(lambda), for lambda a regular weight. We use this to calculate some Ext groups of the form Ext*(del(lambda),Delta(mu)), Ext*(L(lambda),L(mu)), and Ext*(del(lambda),del(mu)), where lambda,mu are regular and Delta(mu) is the Weyl module of highest weight p. We then deduce the projective dimensions and injective dimensions for L(lambda), del(lambda) and Delta(lambda) for lambda a regular weight in associated generalised Schur algebras. We also deduce the global dimension of the Schur algebras for GL(n), S(n, r), when p > n and for S(mp, p) with in an integer.