@article{Friedl2018-03-01Refle-41297,
  year={2018},
  doi={10.1090/proc/13821},
  title={Reflection groups, reflection arrangements, and invariant real varieties},
  number={3},
  volume={146},
  issn={0002-9939},
  journal={Proceedings of the American Mathematical Society},
  pages={1031--1045},
  author={Friedl, Tobias and Riener, Cordian and Sanyal, Raman}
}

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    <dcterms:abstract xml:lang="eng">Let X be a nonempty real variety that is invariant under the action of a reflection group G. We conjecture that if X is defined in terms of the first k basic invariants of G (ordered by degree), then X meets a k-dimensional flat of the associated reflection arrangement. We prove this conjecture for the infinite types, reflection groups of rank at most 3, and F&lt;sub&gt;4&lt;/sub&gt; and we give computational evidence for H&lt;sub&gt;4&lt;/sub&gt;. This is a generalization of Timofte’s degree principle to reflection groups. For general reflection groups, we compute nontrivial upper bounds on the minimal dimension of flats of the reflection arrangement meeting X from the combinatorics of parabolic subgroups. We also give generalizations to real varieties invariant under Lie groups.</dcterms:abstract>
    <dcterms:issued>2018-03-01</dcterms:issued>
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    <dc:creator>Friedl, Tobias</dc:creator>
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    <dcterms:title>Reflection groups, reflection arrangements, and invariant real varieties</dcterms:title>
    <dc:contributor>Sanyal, Raman</dc:contributor>
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    <dc:contributor>Friedl, Tobias</dc:contributor>
    <dc:creator>Riener, Cordian</dc:creator>
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    <dc:contributor>Riener, Cordian</dc:contributor>
    <dc:creator>Sanyal, Raman</dc:creator>
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