Toroidal q-Opers

Abstract

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 $(\overline{GL}(\infty ),q)$-opers with regular singularities and then, by imposing various analytic conditions on singularities, arrive at the desired Bethe equations for toroidal $q$-opers.

55 pages, to appear in the Journal of the Institute of Mathematics of Jussieu

References in corpus (4)

• Baxter Q-Operators and Representations of Yangians
• Lectures on the integrability of the 6-vertex model
• 3d Mirror Symmetry for Instanton Moduli Spaces
• Rationality of capped descendent vertex in $K$-theory

Cited by in corpus (8)

• Quantum toroidal algebras and solvable structures in gauge/string theory
• 3d Mirror Symmetry for Instanton Moduli Spaces
• The Zoo of Opers and Dualities
• On Wronskians and $qq$-systems
• Quantum K-theory and Integrability
• Opers on the projective line, Wronskian relations, and the Bethe Ansatz
• Quantum Toroidal Comodule Algebra of Type $A_{n-1}$ and Integrals of Motion
• Superopers revisited