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We investigate the exact overlaps between eigenstates of integrable spin chains and a special class of states called "integrable initial/final states". These states satisfy a special integrability constraint, and they are closely related to…
Bifractional transformations which lead to quantities that interpolate between other known quantities, are considered. They do not form a group, and groupoids are used to described their mathematical structure. Bifractional coherent states…
Do co-adjoint orbits of Lie groups support a K\"{a}hler structure? We study this question from a point of view derived from coherent states. We examine three examples of Lie groups: the Weyl-Heisenberg group, $\mathrm{SU(2)}$ and…
Adopting a purely group-theoretical point of view, we consider the star product of functions which is associated, in a natural way, with a square integrable (in general, projective) representation of a locally compact group. Next, we show…
The superalgebra eigenstates (SAES) concept is introduced and then applied to find the SAES associated to the $sh(2/2)$ superalgebra, also known as Heisenberg--Weyl Lie superalgebra. This implies to solve a Grassmannian eigenvalue…
The main subject of study of this paper are general properties of HarishChandra algebras and modules with respect wito a pair of algebra and subalgebra, with special focus on the transfer properties to a "spherical subalgebra". We also…
Using ladder operators for the non-linear oscillator with position-dependent effective mass, realization of the dynamic group SU(1,1) is presented. Keeping in view the algebraic structure of the non-linear oscillator, coherent states are…
We study the symmetric powers of four algebras: $q$-oscillator algebra, $q$-Weyl algebra, $h$-Weyl algebra and $U({\mathfrak {sl}}_2)$. We provide explicit formulae as well as combinatorial interpretation for the normal coordinates of…
We give a description of operator algebras of free wreath products in terms of fundamental algebras of graphs of operator algebras as well as an explicit formula for the Haar state. This allows us to deduce stability properties for certain…
First order perturbations of homogeneous and hypersurface orthogonal LRS (Locally Rotationally Symmetric) class II cosmologies with a cosmological constant are considered in the framework of the 1+1+2 covariant decomposition of spacetime.…
We prove that the Moyal product is covariant under linear affine spacetime transformations. From the covariance law, by introducing an $(x,\Theta)$-space where the spacetime coordinates and the noncommutativity matrix components are on the…
The standard and anti-standard ordered operators acting on two-dimensional q-deformed phase space are shown to satisfy algebras which can be called W_\infty. q-star products and q-Moyal brackets corresponding to these algebras are…
In this paper, the Moyal star-product quantization is used to construct the unitary irreducible representations of the Euclidean motion group on 3-dimensions. These unitary representations will come from the representation of its Lie…
We present a classification of homogeneous star products on duals of Lie algebroids in terms of the second Lie algebroid cohomology. Moreover, we extend this classification to projectable star products, i.e., to quantizations compatible…
We establish a connection between the representation theory of certain noncommutative singular varieties and two-dimensional lattice models. Specifically, we consider noncommutative biparametric deformations of the fiber product of two…
The main result of this paper is the proof that all the symmetric products of a (finite) Galois-Maximal space are also Galois-Maximal spaces. This applies to the special case of real algebraic varieties, solving the problem first stated by…
We develop generalized coherent states for a class of nonlinear oscillators with position-dependent effective mass in the context of the Gazeau-Klauder formalism and discuss some of their properties. In order to investigate the temporal…
We first review the introduction of star products in connection with deformations of Poisson brackets and the various cohomologies that are related to them. Then we concentrate on what we have called ``closed star products" and their…
We study continuous phase spaces of single spins and develop a complete description of their time evolution. The time evolution is completely specified by so-called star products. We explicitly determine these star products for general spin…
Let $H$ be any $\PT$ symmetric Schr\"odinger operator of the type $ -\hbar^2\Delta+(x_1^2+...+x_d^2)+igW(x_1,...,x_d)$ on $L^2(\R^d)$, where $W$ is any odd homogeneous polynomial and $g\in\R$. It is proved that $\P H$ is self-adjoint and…