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arXiv · 2011.12003

A diagrammatic approach to string polytopes

Christian Steinert
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Abstract

We prove that for every complex classical group $G$ the string polytope associated to a special reduced decomposition and any dominant integral weight $\lambda$ will be a lattice polytope if and only if the highest weight representation of the Lie algebra of $G$ with highest weight $\lambda$ integrates to a representation of $G$ itself. This affirms an earlier conjecture and shows that every partial flag variety of a complex classical group admits a flat projective degeneration to a Gorenstein Fano toric variety.

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Christian Steinert. 2020-11-24. A diagrammatic approach to string polytopes. https://arxiv.org/abs/2011.12003

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