Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On commuting varieties of nilradicals of Borel subalgebras of reductive
  Lie algebras   Let $G$ be a connected reductive algebraic group defined over an
algebraically closed field $\mathbbm k$ of characteristic zero. We consider the
commuting variety $\mathcal C(\mathfrak u)$ of the nilradical $\mathfrak u$ of
the Lie algebra $\mathfrak b$ of a Borel subgroup $B$ of $G$. In case $B$ acts
on $\mathfrak u$ with only a finite number of orbits, we verify that $\mathcal
C(\mathfrak u)$ is equidimensional and that the irreducible components are in
correspondence with the {\em distinguished} $B$-orbits in $\mathfrak u$. We
observe that in general $\mathcal C(\mathfrak u)$ is not equidimensional, and
determine the irreducible components of $\mathcal C(\mathfrak u)$ in the
minimal cases where there are infinitely many $B$-orbits in $\mathfrak u$.

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The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
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The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
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The categories of this paper are: q-alg