Related papers: "Spread" restricted Young diagrams from a 2D WZNW …
We study finite-dimensional representations of quantum affine algebras of type $B_N$. We show that a module is tame if and only if it is thin. In other words, the Cartan currents are diagonalizable if and only if all joint generalized…
Currents of the SL(N) WZWN model are constrained so that the remaining symmetry is a symmetry of constrained currents as well. Such consistency enables us to study the Poisson structure of constrained SL(N) WZWN models properly. We…
Supersymmetric (SUSY) gauge theories such as the Minimal Supersymmetric Standard Model play a fundamental role in modern particle physics, but have not been verified so far in nature. Here, we show that a SUSY gauge theory with dynamical…
Many disordered systems show a superdiffusive dynamics, intermediate between the diffusive one, typical of a classical stochastic process, and the so called ballistic behaviour, which is generally expected for the spreading in a quantum…
A brief review is given of the integrable realization of affine fusion discovered recently by Korff and Stroppel. They showed that the affine fusion of the $su(n)$ Wess-Zumino-Novikov-Witten (WZNW) conformal field theories appears in a…
We develop the theory of ``branch algebras'', which are infinite-dimensional associative algebras that are isomorphic, up to taking subrings of finite codimension, to a matrix ring over themselves. The main examples come from groups acting…
We define a Wigner distribution function for a one-dimensional finite quantum system, in which the position and momentum operators have a finite (multiplicity-free) spectrum. The distribution function is thus defined on discrete…
Probabilistic diffusion models have achieved state-of-the-art results for image synthesis, inpainting, and text-to-image tasks. However, they are still in the early stages of generating complex 3D shapes. This work proposes Diffusion-SDF, a…
A confining quantum chromodynamics (QCD) model is formulated on the basis of a new general Yang-Mills $SU_3$ symmetry. The general Yang-Mills transformations involve arbitrary vector gauge functions $\omega_\mu(x)$ and Hamilton's…
Let $K$ be a field, $Q$ a quiver, and $\mathcal{A}$ the ideal of the path algebra $KQ$ that is generated by the arrows of $Q$. We present old and new results about the representation theories of the truncations $KQ/\mathcal{A}^L$, $L \in…
Let $\lambda$ be a primitive root of unity of order $\ell$. We introduce a family of finite-dimensional algebras $\{\mathcal{D}_{\lambda,N}(\mathfrak{sl}_2)\}_{N\in\mathbb{N}_0}$ over the complex numbers, such that…
The aim of the paper is to address the behavior in large population of diffusions interacting on a random, possibly diluted and inhomogeneous graph. This is the natural continuation of a previous work, where the homogeneous Erd\H os-R\'enyi…
It is argued that $4d$ $SU(N)$ $\mathcal{N}=4$ SYM has an accumulation line of zero-temperature topologically ordered phases. Each of these phases corresponds to $N$ bound states charged under electromagnetic $\mathbb{Z}^{(1)}_N$ one-form…
In this paper we give an explicit formula for level 1 vertex operators related to $U_q(\widehat{sl}(n))$ as operators on the Fock spaces. We derive also their commutation relations. As an applications we culculate the one point functions of…
We consider an evolving network of a fixed number of nodes. The allocation of edges is a dynamical stochastic process inspired by biological reproduction dynamics, namely by deleting and duplicating existing nodes and their edges. The…
We investigate the spectral and transport properties of many-body quantum systems with conserved charges and kinetic constraints. Using random unitary circuits, we compute ensemble-averaged spectral form factors and linear-response…
We establish a Floquet theorem for a first-order system of differential equations $u'=ru$ where $r$ is an $n\times n$-matrix whose entries are periodic distributions of order $0$. Then we investigate, when $n=1$ and $n=2$, the spectral…
The nucleon is described as a bound state of a quark and an extended diquark. Hereby the notion ``diquark'' refers to the modelling of separable correlations in the two-quark Green's functions. Binding of quarks and diquarks takes place via…
A dynamical system is canonically associated to every Drinfeld double of any affine Kac-Moody group. The choice of the affine Lu-Weinstein-Soibelman double gives a smooth one-parameter deformation of the standard WZW model. In particular,…
The problem of fermion dynamics is studied using the Q-function for fermions. This is a probabilistic phase-space representation, which we express using Majorana operators, so that the phase-space variable is a real antisymmetric matrix. We…