Document Type
Article
Publication Date
1-1-2021
Abstract
A special case of the geometric Langlands correspondence is given by the relationship between solutions of the Bethe ansatz equations for the Gaudin model and opers-connections on the projective line with extra structure. In this paper, we describe a deformation of this correspondence for SL(N). We introduce a difference equation version of opers called q-opers and prove a q-Langlands correspondence between nondegenerate solutions of the Bethe ansatz equations for the XXZ model and nondegenerate twisted q-opers with regular singularities on the projective line. We show that the quantum/classical duality between the XXZ spin chain and the trigonometric Ruijsenaars–Schneider model may be viewed as a special case of the q-Langlands correspondence. We also describe an application of q-opers to the equivariant quantum K-theory of the cotangent bundles to partial flag varieties.
Publication Source (Journal or Book title)
Communications in Mathematical Physics
First Page
641
Last Page
672
Recommended Citation
Koroteev, P., Sage, D., & Zeitlin, A. (2021). (SL(N),q) -Opers, the q-Langlands Correspondence, and Quantum/Classical Duality. Communications in Mathematical Physics, 381 (2), 641-672. https://doi.org/10.1007/s00220-020-03891-1