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arXiv · 2209.11636

On symmetric closed subsets of real affine root systems

Dipnit Biswas·Irfan Habib·R. Venkatesh
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Abstract

Any symmetric closed subset of a finite crystallographic root system must be a closed subroot system. This is not, in general, true for real affine root systems. In this paper, we determine when this is true and also give a very explicit description of symmetric closed subsets of real affine root systems. At the end, using our results, we study the correspondence between symmetric closed subsets of real affine root systems and the regular subalgebras generated by them.

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Dipnit Biswas, Irfan Habib, R. Venkatesh. 2022-09-23. On symmetric closed subsets of real affine root systems. https://arxiv.org/abs/2209.11636

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