A diagrammatic approach to string polytopes
Algebraic Combinatorics, Volume 5 (2022) no. 1, pp. 63-91.

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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DOI: 10.5802/alco.196
Classification: 06A11,  14M25,  17B10,  22E46,  52B05,  52B20
Keywords: String polytopes, marked order polytopes, toric degenerations, flag varieties, representation theory, Lie algebras, classical groups.
Steinert, Christian 1

1 RWTH Aachen University Chair for Algebra and Representation Theory Pontdriesch 10–16 52062 Aachen Germany
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Steinert, Christian. A diagrammatic approach to string polytopes. Algebraic Combinatorics, Volume 5 (2022) no. 1, pp. 63-91. doi : 10.5802/alco.196. https://alco.centre-mersenne.org/articles/10.5802/alco.196/

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