Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exceptional representations of a double quiver of type A, and Richardson
  elements in seaweed Lie algebras   In this paper, we study the set of $\Delta$-filtered modules of
quasi-hereditary algebras arising from quotients of the double of quivers of
type $A$. Our main result is that for any fixed $\Delta$-dimension vector,
there is a unique (up to isomorphism) exceptional $\Delta$-filtered module. We
then apply this result to show that there is always an open adjoint orbit in
the nilpotent radical of a seaweed Lie algebra in $\mathrm{gl}_{n}(\field)$,
thus answering positively in this $\mathrm{gl}_{n}(\field)$ case to a question
raised independently by Michel Duflo and Dmitri Panyushev. An example of a
seaweed Lie algebra in a simple Lie algebra of type $E_{8}$ not admitting an
open orbit in its nilpotent radical is given.

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The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
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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: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: gr-qc
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The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: cond-mat
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The categories of this paper are: econ
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
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The categories of this paper are: nlin