q-Opers, QQ-systems, and Bethe Ansatz II: Generalized Minors

Abstract

In this paper, we describe a certain kind of $q$-connections on a projective line, namely $Z$-twisted $(G,q)$-opers with regular singularities using the language of generalized minors. In part one arXiv:2002.07344 we explored the correspondence between these $q$-connections and $QQ$-systems/Bethe Ansatz equations. Here we associate to a $Z$-twisted $(G,q)$-oper a class of meromorphic sections of a $G$-bundle, satisfying certain difference equations, which we refer to as generalized $q$-Wronskians. Among other things, we show that the $QQ$-systems and their extensions emerge as the relations between generalized minors, thereby putting the Bethe Ansatz equations in the framework of cluster mutations known in the theory of double Bruhat cells.

arXiv comment24 pages. arXiv admin note: text overlap with arXiv:2002.07344

References in corpus (17)

• Integrable Structure of Conformal Field Theory, Quantum KdV Theory and Thermodynamic Bethe Ansatz
• Integrable Structure of Conformal Field Theory II. Q-operator and DDV equation
• Integrable Structure of Conformal Field Theory III. The Yang-Baxter Relation
• Gaudin Model, Bethe Ansatz and Critical Level
• The ODE/IM Correspondence
• Defects and Quantum Seiberg-Witten Geometry
• On Three Dimensional Quiver Gauge Theories and Integrability
• Bethe Ansatz and the Spectral Theory of affine Lie algebra-valued connections I. The simply-laced case
• Bethe Ansatz and the Spectral Theory of affine Lie algebra--valued connections II. The non simply--laced case
• Spectra of quantum KdV Hamiltonians, Langlands duality, and affine opers
• Drinfeld-Sokolov reduction for difference operators and deformations of W-algebras. II. General Semisimple Case
• Cluster algebras and category O for representations of Borel subalgebras of quantum affine algebras
• Discrete Miura Opers and Solutions of the Bethe Ansatz Equations
• Quantum K-theory of Quiver Varieties and Many-Body Systems
• $(SL(N),q)$-opers, the $q$-Langlands correspondence, and quantum/classical duality
• 3d Mirror Symmetry for Instanton Moduli Spaces
• Extended systems of Baxter Q-functions and fused flags I: simply-laced case

Cited by in corpus (1)

• Superopers revisited