Root systems, affine subspaces, and projections

[摘要] We tackle several problems related to a finite irreducible crystallographic root system Fin the real vector space E. In particular, we study the combinatorial structure of the subsets of Phi cut by affine subspaces of 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. (C) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-12-01

[关键词] Root system;Root polytope;Weyl group