Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability of Affine G-varieties and Irreducibility in Reductive Groups   Let $G$ be a reductive affine algebraic group, and let $X$ be an affine
algebraic $G$-variety. We establish a (poly)stability criterion for points
$x\in X$ in terms of intrinsically defined closed subgroups $H_{x}$ of $G$, and
relate it with the numerical criterion of Mumford, and with Richardson and
Bate-Martin-R\"ohrle criteria, in the case $X=G^{N}$. Our criterion builds on a
close analogue of a theorem of Mundet and Schmitt on polystability and allows
the generalization to the algebraic group setting of results of Johnson-Millson
and Sikora about complex representation varieties of finitely presented groups.
By well established results, it also provides a restatement of the non-abelian
Hodge theorem in terms of stability notions.

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The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
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The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
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The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: q-bio