We tackle several problems related to a finite irreducible crystallographic root system Φ in the real vector space E. In particular, we study the combinatorial structure of the subsets of Φ 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.
Root systems, affine subspaces, and projections
Marietti M.
2021-01-01
Abstract
We tackle several problems related to a finite irreducible crystallographic root system Φ in the real vector space E. In particular, we study the combinatorial structure of the subsets of Φ 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.File in questo prodotto:
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