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arXiv · 2109.00944

Root systems, affine subspaces, and projections

Paola Cellini·Mario Marietti
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Abstract

We tackle several problems related to a finite irreducible crystallographic root system $Φ$ in the real vector space $\mathbb E$. In particular, we study the combinatorial structure of the subsets of $Φ$ cut by affine subspaces of $\mathbb E$ and their projections. As byproducts, we obtain easy algebraic combinatorial proofs of refinements of Oshima's Lemma and of a result by Kostant, a partial result towards the resolution of a problem by Hopkins and Postnikov, and new enumerative results on root systems.

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Paola Cellini, Mario Marietti. 2021-09-02. Root systems, affine subspaces, and projections. https://doi.org/10.1016/j.jalgebra.2021.07.035

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