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Reflection groups, reflection arrangements, and invariant real varieties

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Reflection groups, reflection arrangements, and invariant real varieties

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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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