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- W4280521657 abstract "We prove that the Schubert structure constants of the quantum $K$-theory ring of any minuscule flag variety or quadric hypersurface have signs that alternate with codimension. We also prove that the powers of the deformation parameter $q$ that occur in the product of two Schubert classes in the quantum cohomology or quantum $K$-theory ring of a cominuscule flag variety form an integer interval. Our proofs are based on several new results, including an explicit description of the most general non-empty intersection of two Schubert varieties in an arbitrary flag manifold, and a computation of the cohomology groups of any negative line bundle restricted to a Richardson variety in a cominuscule flag variety. We also give a type-uniform proof of the quantum-to-classical theorem, which asserts that the (3-point, genus 0) Gromov-Witten invariants of any cominuscule flag variety are classical triple-intersection numbers on an associated flag variety. Finally, we prove several new results about the geometry and combinatorics related to this theorem." @default.
- W4280521657 created "2022-05-22" @default.
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- W4280521657 date "2022-05-17" @default.
- W4280521657 modified "2023-09-23" @default.
- W4280521657 title "Positivity of minuscule quantum K-theory" @default.
- W4280521657 doi "https://doi.org/10.48550/arxiv.2205.08630" @default.
- W4280521657 hasPublicationYear "2022" @default.
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