Reflection groups, reflection arrangements, and invariant real varieties

Publikationstyp: Zeitschriftenartikel
Publikationsstatus: Published
Autor/innen: Friedl, Tobias; Riener, Cordian; Sanyal, Raman
Erscheinungsjahr: 2018
Erschienen in: Proceedings of the American Mathematical Society ; 146 (2018), 3. - S. 1031-1045. - ISSN 0002-9939. - eISSN 1088-6826
DOI (zitierfähiger Link): https://dx.doi.org/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.
Fachgebiet (DDC): 510 Mathematik
Universitätsbibliographie: Ja

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

@article{Friedl2018-03-01Refle-41297, title={Reflection groups, reflection arrangements, and invariant real varieties}, year={2018}, doi={10.1090/proc/13821}, 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} }

Reflection groups, reflection arrangements, and invariant real varieties Sanyal, Raman Friedl, Tobias Sanyal, Raman 2018-02-12T12:08:32Z 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<sub>4</sub> and we give computational evidence for H<sub>4</sub>. 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. 2018-03-01 Riener, Cordian Riener, Cordian Friedl, Tobias 2018-02-12T12:08:32Z

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