Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Complete Reducibility in Good Characteristic   Let $G$ be a simple algebraic group of exceptional type, over an
algebraically closed field of characteristic $p \ge 0$. A closed subgroup $H$
of $G$ is called $G$-completely reducible ($G$-cr) if whenever $H$ is contained
in a parabolic subgroup $P$ of $G$, it is contained in a Levi subgroup of $P$.
In this paper we determine the $G$-conjugacy classes of non-$G$-cr simple
connected subgroups of $G$ when $p$ is good for $G$. For each such subgroup
$X$, we determine the action of $X$ on the adjoint module $L(G)$ and the
connected centraliser of $X$ in $G$. As a consequence we classify all
non-$G$-cr connected reductive subgroups of $G$, and determine their connected
centralisers. We also classify the subgroups of $G$ which are maximal among
connected reductive subgroups, but not maximal among all connected subgroups.

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The categories of this paper are: chem-ph
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The categories of this paper are: econ
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The categories of this paper are: acc-phys
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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: nlin
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The categories of this paper are: quant-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: cs
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The categories of this paper are: adap-org
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The categories of this paper are: comp-gas