Let Φ be a finite crystallographic irreducible root system and PΦ be the convex hull of the roots in Φ. We give a uniform explicit description of the polytope PΦ, analyze the algebraic-combinatorial structure of its faces, and provide connections with the Borel subalgebra of the associated Lie algebra. We also give several enumerative results.
Root Polytopes and Borel Subalgebras / Cellini, Paola; Marietti, Mario. - In: INTERNATIONAL MATHEMATICS RESEARCH NOTICES. - ISSN 1073-7928. - STAMPA. - 12:(2015), pp. 4392-4420. [10.1093/imrn/rnu070]
Root Polytopes and Borel Subalgebras
MARIETTI, Mario
2015-01-01
Abstract
Let Φ be a finite crystallographic irreducible root system and PΦ be the convex hull of the roots in Φ. We give a uniform explicit description of the polytope PΦ, analyze the algebraic-combinatorial structure of its faces, and provide connections with the Borel subalgebra of the associated Lie algebra. We also give several enumerative results.File in questo prodotto:
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