Related papers: The master T-operator for vertex models with trigo…
For an arbitrary generalized quantum integrable spin chain we introduce a "master T -operator" which represents a generating function for commuting quantum transfer matrices constructed by means of the fusion procedure in the auxiliary…
For integrable inhomogeneous supersymmetric spin chains (generalized graded magnets) constructed employing Y(gl(N|M))-invariant R-matrices in finite-dimensional representations we introduce the master T-operator which is a sort of…
Following the approach of [arXiv:1112.3310], we construct the master T -operator for the quantum Gaudin model with twisted boundary conditions and show that it satisfies the bilinear identity and Hirota equations for the classical KP…
Following the approach of [Alexandrov A., Kazakov V., Leurent S., Tsuboi Z., Zabrodin A., J. High Energy Phys. 2013 (2013), no. 9, 064, 65 pages, arXiv:1112.3310], we show how to construct the master T-operator for the quantum inhomogeneous…
This short note is a review of the intriguing connection between the quantum Gaudin model and the classical KP hierarchy recently established in [1]. We construct the generating function of integrals of motion for the quantum Gaudin model…
We define a tau function for a generic Riemann-Hilbert problem posed on a union of non-intersecting smooth closed curves with jump matrices analytic in their neighborhood. The tau function depends on parameters of the jumps and is expressed…
We consider solvable matrix models. We generalize Harish-Chandra-Itzykson-Zuber and certain other integrals (Gross-Witten integral and integrals over complex matrices) using the notion of tau function of matrix argument. In this case one…
In [1], Nakatsu and Takasaki have shown that the melting crystal model behind the topological strings vertex provides a tau-function of the KP hierarchy after an appropriate time deformation. We revisit their derivation with a focus on the…
We construct different integrable generalizations of the massive Thirring equations corresponding loop algebras $\widetilde{\mathfrak{g}}^{\sigma}$ in different gradings and associated ''triangular'' $R$-operators. We consider the most…
We construct local M-operators for an integrable discrete time version of the classical Heisenberg magnet by convolution of the twisted quantum trigonometric 4$\times$4 R-matrix with certain vectors in its "quantum" space. Components of the…
We derive a new representation for spin-spin correlation functions of the finite XXZ spin-1/2 Heisenberg chain in terms of a single multiple integral, that we call the master equation. Evaluation of this master equation gives rise on the…
In this short review the role of the Hirota equation and the tau-function in the theory of classical and quantum integrable systems is outlined.
We study a special class of operators T satisfying the transmutation relation (Tu)"-qTu=Tu" in the sense of distributions, where q is a locally integrable function, and u belongs to a suitable space of distributions depending on the…
Matrix elements in different representations are connected by quadratic relations. If matrix elements are those of a $\textit{group element}$, i.e. satisfying the property $\Delta(X) = X\otimes X$, then their generating functions obey…
Functional relation for commuting quantum transfer matrices of quantum integrable models is identified with classical Hirota's bilinear difference equation. This equation is equivalent to the completely discretized classical 2D Toda lattice…
The DT-operators are introduced, one for every pair (\mu,c) consisting of a compactly supported Borel probability measure \mu on the complex plane and a constant c>0. These are operators on Hilbert space that are defined as limits in…
The topological zeta function of a matroid is a rational function as well as a valuative invariant of the matroid, encoding rich combinatorial information. We analyze topological zeta functions of matroids from the vantage point of several…
We propose a definition for a Tau function and a spinor kernel (closely related to Baker-Akhiezer functions), where times parametrize slow (of order 1/N) deformations of an algebraic plane curve. This definition consists of a formal…
We study the effective Batalin-Vilkovisky quantization theory for chiral deformation of two dimensional conformal field theories. We establish an exact correspondence between renormalized quantum master equations for effective functionals…
Partition functions of eigenvalue matrix models possess a number of very different descriptions: as matrix integrals, as solutions to linear and non-linear equations, as tau-functions of integrable hierarchies and as special-geometry…