Related papers: On the center of two-parameter (v,t)-quantum group…
In this paper, we give a construction of a (C*-algebraic) quantum Heisenberg group. This is done by viewing it as the dual quantum group of the specific non-compact quantum group (A,\Delta) constructed earlier by the author. Our definition…
We determine the finite-dimensional simple modules for two-parameter quantum groups corresponding to the general linear and special linear Lie algebras gl_n and sl_n, and give a complete reducibility result. These quantum groups have a…
We establish the functional Renormalization Group as an exploratory tool to investigate a possible phase transition between a pre-geometric discrete phase and a geometric continuum phase in quantum gravity. In this paper, based on the…
We define and study the notion of quantum polarity, which is a kind of geometric Fourier transform between sets of positions and sets of momenta. Extending previous work of ours, we show that the orthogonal projections of the covariance…
In this paper we take up the quantal two-centre problem where the Coulomb centres have arbitrary positive charges. In analogy with the symmetric case, treated in the second paper of this series of papers, we use the knowledge on the…
We prove the R-matrix and Drinfeld presentations of the Yangian double in type A are isomorphic. The central elements of the completed Yangian double in type A at the critical level are constructed. The images of these elements under a…
In this study, we introduce the notion of $PL_\delta$-homeomorphisms of $\mathbb{R}^n$. Furthermore, we provide a combinatorial criterion reliant on the vertices and edges of simplicial structures, to determine whether a piecewise-linear…
The rigorous two-center approach based on the dual-kinetically balanced finite-basis-set expansion is applied to one-electron, heteronuclear diatomic Bi-Au, U-Pb, and Cf-U quasimolecules. The obtained $1\sigma$ ground-state energies are…
The entanglement entropy of a pure quantum state of a bipartite system is defined as the von Neumann entropy of the reduced density matrix obtained by tracing over one of the two parts. Critical ground states of local Hamiltonians in one…
Let G be a real semi-simple Lie group and H a closed subgroup which admits an open orbit on the flag manifold of a minimal parabolic subgroup. Let V be a Harish-Chandra module. A sharp finite bound is given for the dimension of the space of…
The so-called two-vertex model of loop quantum gravity has been analytically studied in the past within a U($N$) symmetry-reduced sector leading to a cosmological interpretation. In this work we study the simplest non-trivial two-vertex…
This paper suveys some recent algebraic developments in two parameter Quantum deformations and their Nonstandard (or Jordanian) counterparts. In particular, we discuss the contraction procedure and the quantum group homomorphisms associated…
Geometric quantum mechanics aims to express the physical properties of quantum systems in terms of geometrical features preferentially selected in the space of pure states. Geometric characterisations are given here for systems of one, two,…
We develop an elementary algebraic method to compute the center of the principal block of a small quantum group associated with a complex semisimple Lie algebra at a root of unity. The exemplary case of $\mathfrak{sl}_3$ is computed…
We examine from an algebraic point of view some families of unitary group representations that arise in mathematical physics and are associated to contraction families of Lie groups. The contraction families of groups relate different real…
The purpose of this paper is to apply deformation quantization to the study of the coadjoint orbit method in the case of real reductive groups. We first prove some general results on the existence of equivariant deformation quantization of…
This paper gives elements in the (skew) center of the generalized quantum group corresponding to its irreducible finite dimensional modules. Finally we give a conjecture stating that those must form a basis of the center.
Collective center-of-mass variables are introduced in the Lagrangian formalism of the relativistic classical mechanics of directly interacting particles. It is shown that the transition to the Hamiltonian formalism leads to the…
Centers of categories capture the natural operations on their objects. Homotopy coherent centers are introduced here as an extension of this notion to categories with an associated homotopy theory. These centers can also be interpreted as…
The nondivergence of the generalized Gr\"uneisen ratio (GR) at a quantum critical point (QCP) has been proposed to be a universal thermodynamic signature of self-duality. In this work, we study how the Kramers-Wannier-type self-duality…