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TOROIDAL q-OPERS

Published online by Cambridge University Press:  18 June 2021

Peter Koroteev Open the ORCID record for Peter Koroteev [Opens in a new window]  and
Anton M. Zeitlin
Peter Koroteev
Affiliation:
Department of Mathematics, University of California, Berkeley, CA 94720, USA
Anton M. Zeitlin
Affiliation:
Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USA IPME RAS, St. Petersburg, Russia
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Abstract

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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.

Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 22 , Issue 2 , March 2023 , pp. 581 - 642
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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