$$({{,mathrm{mathrm {SL}},}}(N),q)$$ ( SL ( N
$$({{,mathrm{mathrm {SL}},}}(N),q)$$
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SL
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$$({{,mathrm{mathrm {SL}},}}(N),q)$$ ( SL ( N
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
A. Zeitlin
中科院分区：
文献类型：
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作者：
Peter Koroteev;Daniel S. Sage;A. Zeitlin
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 $${{,mathrm{mathrm {SL}},}}(N)$$ 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.
