Reflection groups, reflection arrangements, and invariant real varieties

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2018
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Friedl, Tobias
Sanyal, Raman
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Proceedings of the American Mathematical Society. 2018, 146(3), pp. 1031-1045. ISSN 0002-9939. eISSN 1088-6826. Available under: doi: 10.1090/proc/13821
Zusammenfassung

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 F4 and we give computational evidence for H4. 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.

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510 Mathematik
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ISO 690FRIEDL, Tobias, Cordian RIENER, Raman SANYAL, 2018. Reflection groups, reflection arrangements, and invariant real varieties. In: Proceedings of the American Mathematical Society. 2018, 146(3), pp. 1031-1045. ISSN 0002-9939. eISSN 1088-6826. Available under: doi: 10.1090/proc/13821
BibTex
@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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