Related papers: On Wronskians and $qq$-systems
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…
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,…
The relation between special connections on the projective line, called Miura opers, and the spectra of integrable models of Gaudin type provides an important example of the geometric Langlands correspondence. The possible generalization of…
Q-systems provide an efficient way of solving Bethe equations. We formulate here Q-systems for both the isotropic and anisotropic open Heisenberg quantum spin-1/2 chains with diagonal boundary magnetic fields. We check these Q-systems using…
In in a nutshell, the classical geometric $q$-Langlands duality can be viewed as a correspondence between the space of $(G,q)$-opers and the space of solutions of $^L\mathfrak{g}$ XXZ Bethe Ansatz equations. The latter describe spectra of…
It is well-known that the spectra of the Gaudin model may be described in terms of solutions of the Bethe Ansatz equations. A conceptual explanation for the appearance of the Bethe Ansatz equations is provided by appropriate $G$-opers:…
We introduce the notions of $(G,q)$-opers and Miura $(G,q)$-opers, where $G$ is a simply-connected complex simple Lie group, and prove some general results about their structure. We then establish a one-to-one correspondence between the set…
We formulate $Q$-systems for the closed XXZ, open XXX and open quantum-group-invariant XXZ quantum spin chains. Polynomial solutions of these $Q$-systems can be found efficiently, which in turn lead directly to the admissible solutions of…
We introduce twisted quantum $K$-rings, defined via twisted $K$-theoretic Gromov-Witten invariants. We develop a toolkit for computing relations by adapting some results about ordinary quantum K rings to our setting, and discuss some…
The $Q$-system is an efficient method for finding complete physical solutions of Bethe ansatz equations, but so far its application has been confined to systems possessing $U(1)$ symmetry. We extend the rational $Q$-system framework to…
We define the q-deformed Gelfand-Dickey bracket on the space of q-pseudodifference symbols which agrees with the Poisson Virasoro algebra of E.Frenkel and N.Reshetikhin and its generalizations and prove its uniqueness (in a natural class of…
Taking the isotropic limit in a recent representation theoretic construction of Baxter's Q-operators for the XXZ model with quasi-periodic boundary conditions we obtain new results for the XXX model. We show that quasi-periodic boundary…
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…
We consider the Schr\"odinger operators which are constructed from the $\lambda$-opers corresponding to solutions of the $\widehat{\mathfrak{sl}}_2$ Gaudin Bethe Ansatz equations. We define and study the connection coefficients called the…
We show that the relations which define the algebras of the quantum Euclidean planes $\b{R}^N_q$ can be expressed in terms of projections provided that the unique central element, the radial distance from the origin, is fixed. The resulting…
We develop a perturbation method that generalizes an approach proposed recently to treat velocity--dependent quantum--mechanical models. In order to test present approach we apply it to some simple trivial and nontrivial examples.
We study the structure of abelian extensions of the group $L_qG$ of $q$-differentiable loops (in the Sobolev sense), generalizing from the case of central extension of the smooth loop group. This is motivated by the aim of understanding the…
We propose the notion of q-characters for finite-dimensional representations of quantum affine algebras. It is motivated by our theory of deformed W-algebras. We show that the q-characters give rise to a homomorphism from the Grothendieck…
In \cite{GS1} the notion of braided Yangians of Reflection Equation type was introduced. Each of these algebras is associated with an involutive or Hecke symmetry $R$. Besides, the quantum analogs of certain symmetric polynomials…
This work investigates the intricate relationship between the q-boson model, a quantum integrable system, and classical integrable systems such as the Toda and KP hierarchies. Initially, we analyze scalar products of off-shell Bethe states…