Strongly dominant weight polytopes are cubes

2023/11/27 by Gaston Burrull, Tao Gui, Burrull, Gaston +3 · 2 citations
Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2311.16022

Abstract

For any root system of rank r, we study the "dominant weight polytope" P^λ associated with a strongly dominant weight λ. We prove that P^λ is combinatorially equivalent to the r-dimensional cube. As an application, we give a new proof of the known formulas for Betti numbers of Peterson varieties in classical Lie types.

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• The graph of implicit edge dependencies for indecomposability and beyond
• Totally nonnegative Peterson variety and strongly dominant weight polytope

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