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arXiv · 2311.16022

Strongly dominant weight polytopes are cubes

Gaston Burrull·Tao Gui·Hongsheng Hu
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Abstract

For any root system of rank $r$, we study the "dominant weight polytope" $P^\lambda$ associated with a strongly dominant weight $\lambda$. We prove that $P^\lambda$ 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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Gaston Burrull, Tao Gui, Hongsheng Hu. 2023-11-27. Strongly dominant weight polytopes are cubes. https://arxiv.org/abs/2311.16022

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