Explicit description of certain 3-point K-theoretic Gromov-Witten invariants for flag manifolds

[2608.00359] Explicit description of certain 3-point K-theoretic Gromov-Witten invariants for flag manifolds Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Quantum Algebra arXiv:2608.00359 (math) [Submitted on 1 Aug 2026 ( v1 ), last revised 15 Aug 2026 (this version, v2)] Title: Explicit description of certain 3-point K-theoretic Gromov-Witten invariants for flag manifolds Authors: Satoshi Naito , Daisuke Sagaki View a PDF of the paper titled Explicit description of certain 3-point K-theoretic Gromov-Witten invariants for flag manifolds, by Satoshi Naito and Daisuke Sagaki View PDF HTML (experimental) Abstract: We give an explicit description, in terms of the quantum Bruhat graph, of the (torus-equivariant) 3-point, genus 0, $K$-theoretic Gromov-Witten invariants $\langle \mathcal{O}(- \lambda), \mathcal{O}^{w}, \mathcal{O}_{u} \rangle_{d}$ for the (full) flag manifold $X = G/B$, where $\mathcal{O}(- \lambda)$ denotes the class in the (torus-equivariant) $K$-theory ring $K_{T}(X)$ of $X$ of the line bundle $\mathcal{O}_{X}(- \lambda) = G \times_{B} \mathbb{C}_{\lambda}$ over $X = G/B$ associated to a weight $\lambda \in W \varpi_i$ lying in the Weyl group orbit of a minuscule fundamental weight $\varpi_i$, and $\mathcal{O}_{u}$, $\mathcal{O}^{w}$ are the Schubert and opposite Schubert classes in $K_{T}(X)$ for $u, w \in W$. This result can be thought of as a partial generalization of the quantum $K$-theoretic divisor axiom, which we obtained in our previous work; our proof utilizes a generalization of the Chevalley formula in the (torus-equivariant) quantum $K$-theory ring $QK_{T}(X)$ of $X$, which computes the quantum product with the line bundle class $\mathcal{O}(- \lambda)$ associated to the weight $\lambda$ above. Subjects: Quantum Algebra (math.QA) ; Algebraic Geometry (math.AG); Combinatorics (math.CO); K-Theory and Homology (math.KT); Representation Theory (math.RT) MSC classes: (2020) Primary 14N35, Secondary 14M15, 14N15, 14N10, 05E14 Cite as: arXiv:2608.00359 [math.QA] (or arXiv:2608.00359v2 [math.QA] for this version) https://doi.org/10.48550/arXiv.2608.00359 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Daisuke Sagaki [ view email ] [v1] Sat, 1 Aug 2026 00:14:54 UTC (25 KB) [v2] Sat, 15 Aug 2026 02:03:07 UTC (26 KB) Full-text links: Access Paper: View a PDF of the paper titled Explicit description of certain 3-point K-theoretic Gromov-Witten invariants for flag manifolds, by Satoshi Naito and Daisuke Sagaki View PDF HTML (experimental) TeX Source view license Current browse context: math.QA < prev | next > new | recent | 2026-08 Change to browse by: math math.AG math.CO math.KT math.RT References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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