Year: 2025
Type: preprint
Abstract: Let $\mathfrak{g} = \bigoplus_{i \in \mathbb{Z} /m \mathbb{Z}} \mathfrak{g}_i$ be a periodically graded semisimple complex Lie algebra. In this note, we give a uniform proof of the recent result by W. de Graaf and H. V. Lê that the hyperplane arrangement determined by the restrictions of the roots of $\mathfrak{g}$ to a Cartan subspace $\mathfrak{c} \subset \mathfrak{g}_1$ coincides with the hyperplane arrangement of (complex) reflections of the little Weyl group of $\mathfrak{g} = \bigoplus_{i \in \mathbb{Z} /m \mathbb{Z}} \mathfrak{g}_i$.
Source: arXiv (Cornell University)
Authors: Ambrosio, Filippo, Santi, Andrea
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7080182005
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