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arXiv · 2510.21653

Quantum Difference Equations for Grassmannians

Xingyu Cheng·Reese Lance·Nikhil Nagabandi·Andrey Smirnov
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Abstract

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.

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Xingyu Cheng, Reese Lance, Nikhil Nagabandi, Andrey Smirnov. 2025-10-24. Quantum Difference Equations for Grassmannians. https://arxiv.org/abs/2510.21653

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