THE MODULAR REPRESENTATION-THEORY OF Q-SCHUR ALGEBRAS

We developed some basic theory of characteristic zero modular representations of q-Schur algebras. We described a basis of the q-Schur algebra in terms of the relative norm which was first introduced by P. Hoefsmit and L. Scott, and studied the product of two such basis elements. We also defined the defect group of a primitive idempotent in a q-Schur algebra and showed that such a defect group is just the vertex of the corresponding indecomposable H(F)-module.