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 / Cellini, P.; Marietti, M.. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - STAMPA. - 587:(2021), pp. 310-335. [10.1016/j.jalgebra.2021.07.035]
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
