Good l-filtrations for q-GL_3(k)

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

2005-08-22

arxiv.org/abs/math/0508404v1

Mathematics

Representation Theory

2 figures, 33 pages, uses xypic

Scientific paper

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, $\hat{Z}(\lambda)$, for the infinitesimal group $G_1B$. We induce this structure to $G$ to obtain a good $l$-filtration of certain induced modules, $\nabla(\lambda)$, for $G$. We also determine the homomorphisms between induced modules for $G$.

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