Root systems, affine subspaces, and projections

Abstract

We tackle several problems related to a finite irreducible crystallographic root system $\Phi$ in the real vector space $\mathbb{E}$. In particular, we study the combinatorial structure of the subsets of $\Phi$ 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.

arXiv commentThis manuscript version is made available under the CC-BY-NC-ND 4.0 license. Manuscript has been accepted to Journal of Algebra

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