Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Short antichains in root systems, semi-Catalan arrangements, and
  B-stable subspaces   Let $\be$ be a Borel subalgebra of a complex simple Lie algebra $\g$. An
ideal of $\be$ is called ad-nilpotent, if it is contained in $[\be,\be]$. The
generators of an ad-nilpotent ideal give rise to an antichain in the poset of
positive roots, and the whole theory can be expressed in a combinatorial
fashion, in terms of antichains. The aim of this paper is to present a
refinement of the enumerative theory of ad-nilpotent ideals for the case in
which $\g$ has roots of different length. An antichain is called short, if it
consists of short roots. We obtain, for short antichains, analogues of all
results known for the usual antichains.

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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: hep-th
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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: q-bio
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The categories of this paper are: quant-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
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The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph