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arXiv 2011.120032020-11-24math.RTmath.CO

A diagrammatic approach to string polytopes

Christian Steinert

备注：: 29 pages, 12 figures

英文摘要：

We prove that for every complex classical group $G$ the string polytope associated to a special reduced decomposition and any dominant integral weight $λ$ will be a lattice polytope if and only if the highest weight representation of the Lie algebra of $G$ with highest weight $λ$ 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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