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      Root systems, affine subspaces, and projections

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          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.

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          Author and article information

          Journal
          02 September 2021
          Article
          10.1016/j.jalgebra.2021.07.035
          2109.00944
          cc206f17-8c3b-4f94-aeac-a557fa612c8c

          http://creativecommons.org/licenses/by-nc-nd/4.0/

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          This manuscript version is made available under the CC-BY-NC-ND 4.0 license. Manuscript has been accepted to Journal of Algebra
          math.CO math.RT

          Combinatorics, Algebra

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