Good l-filtrations for q-GL3(k)

Let k be an algebraically closed field of characteristic p, possibly zero, and G=q-GL3(k), the quantum group of three by three matrices as defined by Dipper and Donkin. We may also take G to be GL3(k). We first determine the extensions between simple G-modules for both G and G1, the first Frobenius kernel of G. We then determine the submodule structure of certain induced modules, , for the infinitesimal group G1B. We induce this structure to G to obtain a good l-filtration of certain induced modules, ∇(λ), for G. We also determine the homomorphisms between these induced modules for G.