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Newton-Okounkov polytopes of Schubert varieties arising from cluster structures

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arxiv 2002.09912 v3 pith:GK6JB4RC submitted 2020-02-23 math.RT math.AGmath.CO

Naoki Fujita , Hironori Oya This is my paper · ORCID
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keywords bodiesnewton-okounkovpolytopesvarietiesclustertheoryschuberttoric
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The theory of Newton-Okounkov bodies is a generalization of that of Newton polytopes for toric varieties, and it gives a systematic method of constructing toric degenerations of projective varieties. In this paper, we study Newton-Okounkov bodies of Schubert varieties from the theory of cluster algebras. We construct Newton-Okounkov bodies using specific valuations which generalize extended g-vectors in cluster theory, and discuss how these bodies are related to string polytopes and Nakashima-Zelevinsky polytopes.

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  1. Crystals and quantum twist automorphisms

    math.RT 2025-07 conditional novelty 7.0 of 10

    The quantum twist automorphism is computed through PBW and string parametrizations of localized crystals, with explicit minuscule Young diagram rules and a closed periodicity formula in type A.

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