Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Representation Theoretic Explanation of the Borcea-Br\"and\'en
  Characterization   In 2009, Borcea and Br\"and\'en characterize all linear operators on
multivariate polynomials which preserve the property of being non-vanishing
(stable) on products of prescribed open circular regions. We give a
representation theoretic interpretation of their findings, which generalizes
and simplifies their result and leads to a conceptual unification of many
related results in polynomial stability theory. At the heart of this
unification is a generalized Grace's theorem which addresses polynomials whose
roots are all contained in some real interval or ray. This generalization
allows us to extend the Borcea-Br\"and\'en result to characterize a certain
subclass of the linear operators which preserve such polynomials.

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The categories of this paper are: chao-dyn
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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: nucl-th
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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: atom-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
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The categories of this paper are: solv-int
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The categories of this paper are: stat
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The categories of this paper are: astro-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: econ