Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Adjoint quotients of reductive groups   Let $\rG$ be a reductive group over a commutative ring $k$. In this article,
we prove that the adjoint quotient $\adqG$ is stable under base change.
Moreover, if $\rG$ has a maximal torus $\rT$, then the adjoint quotient of the
torus $\rT$ by its Weyl group will be isomorphic to $\adqG$. Then we focus on
the semisimple simply connected group $\rG$ of the constant type. In this case,
$\adqG$ is isomorphic to the Weil restriction $\underset{\rD/\spec
k}{\prod}\aff^{1}_\rD$, where $\rD$ is the Dynkin scheme of $\rG$. Then we
prove that for such $\rG$, the Steinberg's cross-section can be defined over
$k$ if $\rG$ is quasi-split and without $\rA_{2m}$-type components

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The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
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The categories of this paper are: cs
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The categories of this paper are: dg-ga
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin