Quantum $K$-theoretic divisor axiom for flag manifolds
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915587987341312 |
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| author | Lenart, Cristian Naito, Satoshi Sagaki, Daisuke Mihalcea, Leonardo C. Xu, Weihong |
| author_facet | Lenart, Cristian Naito, Satoshi Sagaki, Daisuke Mihalcea, Leonardo C. Xu, Weihong |
| contents | We prove an identity for (torus-equivariant) 3-point, genus 0, $K$-theoretic Gromov-Witten invariants of flag manifolds $G/P$, which can be thought of as a replacement for the ``divisor axiom'' in their (torus-equivariant) quantum $K$-theory. This identity enables us to compute these invariants when two insertions are Schubert classes and the other a Schubert divisor class. Our type-independent proof utilizes the Chevalley formula for the (torus-equivariant) quantum $K$-theory ring of flag manifolds, which computes multiplications by Schubert divisor classes in terms of the quantum Bruhat graph. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_16150 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum $K$-theoretic divisor axiom for flag manifolds Lenart, Cristian Naito, Satoshi Sagaki, Daisuke Mihalcea, Leonardo C. Xu, Weihong Quantum Algebra Algebraic Geometry Combinatorics K-Theory and Homology Representation Theory Primary 14N35, Secondary 14M15, 14N15, 14N10, 05E14 We prove an identity for (torus-equivariant) 3-point, genus 0, $K$-theoretic Gromov-Witten invariants of flag manifolds $G/P$, which can be thought of as a replacement for the ``divisor axiom'' in their (torus-equivariant) quantum $K$-theory. This identity enables us to compute these invariants when two insertions are Schubert classes and the other a Schubert divisor class. Our type-independent proof utilizes the Chevalley formula for the (torus-equivariant) quantum $K$-theory ring of flag manifolds, which computes multiplications by Schubert divisor classes in terms of the quantum Bruhat graph. |
| title | Quantum $K$-theoretic divisor axiom for flag manifolds |
| topic | Quantum Algebra Algebraic Geometry Combinatorics K-Theory and Homology Representation Theory Primary 14N35, Secondary 14M15, 14N15, 14N10, 05E14 |
| url | https://arxiv.org/abs/2505.16150 |