T-and Y-systems are ubiquitous structures in classical and quantum integrable systems.
They are difference equations having a variety of aspects related to commuting transfer …

We review recent progress in understanding the notion of locality in integrable quantum
lattice systems. The central concept concerns the so-called quasilocal conserved quantities …

The goals of this paper are two-fold. First, we prove, for an arbitrary finite root system D, the
periodicity conjecture of Al. B. Zamolodchikov [24] that concerns Y-systems, a particular …

Anomalous finite-temperature transport has recently been observed in numerical studies of
various integrable models in one dimension; these models share the feature of being …

We show how aspects of the R-charge of N= 2 CFTs in four dimensions are encoded in the q-
deformed Kontsevich-Soibelman monodromy operator, built from their dyon spectra. In …

We study a system of functional relations among a commuting family of row-to-row transfer
matrices in solvable lattice models. The role of exact sequences of the finite-dimensional …

We study the dilogarithm identities from algebraic, analytic, asymptotic, K-theoretic,
combinatorial and representation-theoretic points of view. We prove that a lot of dilogarithm …

This is an introduction to some aspects of Fomin-Zelevinsky's cluster algebras and their links
with the representation theory of quivers and with Calabi-Yau triangulated categories. It is …

A bstract In presence of a static pair of sources, the spectrum of low-lying states of whatever
confining gauge theory in D space-time dimensions is described, at large source …

We introduce a fermionic formula associated with any quantum affine algebra U q (XN (r).
Guided by the interplay between corner transfer matrix and the Bethe ansatz in solvable …