Preprint
Good lfiltrations for qGL_3(k)
Alison Parker
Abstract
Let k be an algebraically closed field of characteristic p,
possibly zero, and G=qGL_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 Gmodules 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
lfiltration of certain induced modules, ∇(λ), for
G. We also determine the homomorphisms between induced modules
for G.
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