  We continue the development of the homological theory of quantum general
linear groups previously considered by the first author. The development is
used to transfer information to the representation theory of quantised Schur
algebras. The acyclicity of induction from some rank-one modules for quantised
Borel-Schur subalgebras is deduced. This is used to prove the exactness of the
complexes recently constructed by Boltje and Maisch, giving resolutions of the
co-Specht modules for Hecke algebras.
