## Good l-filtrations for q-GL_3(k)

### Alison Parker

#### Abstract

Let k be an algebraically closed field of characteristic p, possibly zero, and G=q-GL_3(k), the quantum group of three by three matrices as defined by Dipper and Donkin. We may also take G to be GL_3(k). We first determine the extensions between simple G-modules for both G and G_1, the first Frobneius kernel of G. We then determine the submodule structure of certain induced modules, \hat{Z}(λ), for the infinitesimal group G_1B. 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 induced modules for G.
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 Thursday, April 28, 2005