TOROIDAL q-OPERS

We define and study the space of q-opers associated with Bethe equations for integrable models of XXZ type with quantum toroidal algebra symmetry. Our construction is suggested by the study of the enumerative geometry of cyclic quiver varieties, in particular the ADHM moduli spaces. We define $\left...

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Bibliographic Details
Published in:Journal of the Institute of Mathematics of Jussieu 2023-03, Vol.22 (2), p.581-642
Main Authors: Koroteev, Peter, Zeitlin, Anton M.
Format: Article
Language:English
Subjects:
Algebra
Eigenvalues
Mathematics
Singularity (mathematics)
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Summary:We define and study the space of q-opers associated with Bethe equations for integrable models of XXZ type with quantum toroidal algebra symmetry. Our construction is suggested by the study of the enumerative geometry of cyclic quiver varieties, in particular the ADHM moduli spaces. We define $\left (\overline {GL}(\infty ),q\right )$ -opers with regular singularities and then, by imposing various analytic conditions on singularities, arrive at the desired Bethe equations for toroidal q-opers.
ISSN:1474-7480
1475-3030
DOI:10.1017/S1474748021000220