Quantum Difference Equations for Grassmannians
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912669111418880 |
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| author | Cheng, Xingyu Lance, Reese Nagabandi, Nikhil Smirnov, Andrey |
| author_facet | Cheng, Xingyu Lance, Reese Nagabandi, Nikhil Smirnov, Andrey |
| contents | We consider quantum difference equation (QDE) for equivariant quantum K-theory of the Grassmannian. In this paper we obtain a solution to the QDE and use the solution to asymptotically derive the Bethe ansatz equations. In the limit, we obtain similar results for the cohomological analogue. For both cases, we describe the nonequivariant solutions as well. As an application, we identify the quantum K-theory ring of $\mathrm{Gr}(k,n)$ with a quantum 5 vertex XXZ integrable spin chain. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_21653 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum Difference Equations for Grassmannians Cheng, Xingyu Lance, Reese Nagabandi, Nikhil Smirnov, Andrey Mathematical Physics Algebraic Geometry Combinatorics Quantum Algebra Representation Theory We consider quantum difference equation (QDE) for equivariant quantum K-theory of the Grassmannian. In this paper we obtain a solution to the QDE and use the solution to asymptotically derive the Bethe ansatz equations. In the limit, we obtain similar results for the cohomological analogue. For both cases, we describe the nonequivariant solutions as well. As an application, we identify the quantum K-theory ring of $\mathrm{Gr}(k,n)$ with a quantum 5 vertex XXZ integrable spin chain. |
| title | Quantum Difference Equations for Grassmannians |
| topic | Mathematical Physics Algebraic Geometry Combinatorics Quantum Algebra Representation Theory |
| url | https://arxiv.org/abs/2510.21653 |