Related papers: Asymmetric Twin Representation: the Transfer Matri…
The asymptotic symmetry algebra of four-dimensional Einstein gravity in the asymptotically flat context has been shown recently to be the direct sum of the Poincar\'e algebra and of an infinite-dimensional abelian algebra (with central…
Quantum systems with discrete symmetries can usually be desymmetrized, but this strategy fails when considering transport in open systems with a symmetry that maps different openings onto each other. We investigate the joint probability…
Modulated symmetries are internal symmetries that act in a non-uniform, spatially modulated way and are generalizations of, for example, dipole symmetries. In this paper, we systematically study the gauging of finite Abelian modulated…
The off-diagonal Bethe Ansatz method [1] is used to revisit the periodic XXX Heisenberg spin-1/2 chain. It is found that the spectrum of the transfer matrix can be characterized by an inhomogeneous T-Q relation, a natural but nontrivial…
It has been recently discovered in the context of the six vertex or XXZ model in the fundamental representation that new symmetries arise when the anisotropy parameter $(q+q^{-1})/2$ is evaluated at roots of unity $q^{N}=1$. These new…
For the proposed duality relating a family of N=4 superconformal coset models to a certain supersymmetric higher spin theory on AdS_3, the asymptotic symmetry algebra of the bulk description is determined. It is shown that, depending on the…
We develop the representation theory of shifted quantum affine algebras $\mathcal{U}_q^\mu(\hat{\mathfrak{g}})$ and of their truncations which appeared in the study of quantized K-theoretic Coulomb branches of 3d $N = 4$ SUSY quiver gauge…
We study the Hilbert space of the Class 5 model described in arXiv:1904.12005. Despite being integrable, neither its transfer matrix nor its Hamiltonian are diagonalisable, meaning that the usual Algebraic Bethe Ansatz does not provide the…
The purpose of this paper is to investigate an algebraic version of the double complex transfer, in particular the classes in the two-line of the Adams-Novikov spectral sequence which are the image of comodule primitives of the MU-homology…
We present a systematic recipe for generating and classifying duality transformations in one-dimensional quantum lattice systems. Our construction emphasizes the role of global symmetries, including those described by (non)-abelian groups…
The quantum affine $\CU_q (\hat{sl(2)}) $ symmetry is studied when $q^2$ is an even root of unity. The structure of this algebra allows a natural generalization of N=2 supersymmetry algebra. In particular it is found that the momentum…
The fused six-vertex models with open boundary conditions are studied. The Bethe ansatz solution given by Sklyanin has been generalized to the transfer matrices of the fused models. We have shown that the eigenvalues of transfer matrices…
We call an operator algebra A {\em reversible} if A with reversed multiplication is also an abstract operator algebra (in the modern operator space sense). This class of operator algebras is intimately related to the {\em symmetric operator…
Let $\mathfrak{g}$ be a complex simple Lie algebra and $U_q(\hat{\mathfrak{g}})$ the corresponding quantum affine algebra. We prove that every irreducible finite-dimensional $U_q(\hat{\mathfrak{g}})$-module gives rise to a family of…
This note is an attempt to extend "Geometric Langlands Conjecture" from algebraic curves to algebraic surfaces. We introduce certain Hecke-type operators on vector bundles on an algebraic surface. The crucial observation is that the algebra…
A connection between integrability properties and general statistical properties of the spectra of symmetric transfer matrices of the asymmetric eight-vertex model is studied using random matrix theory (eigenvalue spacing distribution and…
We prove a Berger-type theorem which asserts that if the orthogonal subgroup generated by the torsion tensor (pulled back to a point by parallel transport) of a metric connection with skew-symmetric torsion is not transitive on the sphere,…
The Hamiltonian of the $N$-state clock model is written in terms of a coupled Temperley-Lieb (TL) algebra defined by $N-1$ types of TL generators. This generalizes a previous result for $N=3$ obtained by J. F. Fjelstad and T. M\r{a}nsson…
We define new diagram algebras providing a sequence of multiparameter generalisations of the Temperley-Lieb algebra, suitable for the modelling of dilute lattice systems of two-dimensional Statistical Mechanics. These algebras give a…
This work provides a comprehensive theoretical framework for understanding the symmetry properties of High-Resolution NMR spectra. We analyze the conditions under which a spectrum exhibits mirror symmetry (palindromicity). We demonstrate…