Related papers: Conformal super Virasoro algebra: matrix model and…
The quantum double construction of a $q$-deformed boson algebra possessing a Hopf algebra structure is carried out explicitly. The $R$-matrix thus obtained is compared with the existing literature.
We investigate, in some details, symplectic equivalence between several conformal classes of Lorentz metrics on the hyperboloid of one sheet $H^{1,1} \cong T \times T - \Delta$ and affine coadjoint orbits of the group $Diff_+(\Delta)$ of…
We obtain a closed form expression of the universal T-matrix encapsulating the duality of the quantum superalgebra U_q[osp(1/2)] and the corresponding supergroup OSp_q(1/2). The classical q-->1 limit of this universal T-matrix yields the…
The one-dimensional Hubbard model is an exceptional integrable spin chain which is apparently based on a deformation of the Yangian for the superalgebra gl(2|2). Here we investigate the quantum-deformation of the Hubbard model in the…
We extend the differential form representation of N = (n,n) supersymmetric quantum mechanics to the superconformal case. We identify the superalgebras occurring for n = 1,2,4, give necessary and sufficient conditions for their existence,…
We undertake a study of transposed \delta-Poisson (super)algebra structures on the Virasoro-like algebra and its Kantor Lie-double -- the latter being constructed via Kantor's procedure. This work leads to the finding that, whereas…
Certain integrable models are described by pairs (X,Y) of ADET Dynkin diagrams. At high energy these models are expected to have a conformally invariant limit. The S-matrix of the model determines algebraic equations, whose solutions are…
A class of transformations of $R_q$-matrices is introduced such that the $q\to 1$ limit gives explicit nonstandard $R_{h}$-matrices. The transformation matrix is singular itself at $q\to 1$ limit. For the transformed matrix, the…
We will demonstrate how calculations in toric geometry can be used to compute quantum corrections to the relations in the chiral ring for certain gauge theories. We focus on the gauge theory of the del Pezzo 2, and derive the chiral ring…
A randomly generated complex symmetric matrix using Adaptive Monte Carlo method, is taken as a general form of Majorana neutrino mass matrix, which is diagonalized by the use of eigenvectors. We extract all the neutrino oscillation…
We show that quantum curves arise in infinite families and have the structure of singular vectors of a relevant symmetry algebra. We analyze in detail the case of the hermitian one-matrix model with the underlying Virasoro algebra, and the…
The deformed algebra $\cal{A(R)}$, depending upon a Yang-Baxter R- matrix, is considered. The conditions under which the algebra is associative are discussed for a general number of oscillators. Four types of solutions satisfying these…
In this paper, we investigate $(p, q)$-derivations in both general algebras and Banach algebras. Our main result extends the Singer-Wermer theorem to $(p, q)$-derivations, proving that their ranges are contained in the radical of the…
The dispersion relation for planar N=4 supersymmetric Yang-Mills is identified with the Casimir of a quantum deformed two-dimensional kinematical symmetry, E_q(1,1). The quantum deformed symmetry algebra is generated by the momentum, energy…
After a short introduction on Clifford algebras of polynomials, we give a general method of constructing a matrix representation. This process of linearization leads naturally to two fundamental structures: the generalized Clifford algebra…
Superconformal symmetry in six-dimensions is analyzed in terms of coordinate transformations on superspace. A superconformal Killing equation is derived and its solutions are identified in terms of supertranslations, dilations, Lorentz…
Affine transformations (dilatations and translations) are used to define a deformation of one-dimensional $N=2$ supersymmetric quantum mechanics. Resulting physical systems do not have conserved charges and degeneracies in the spectra.…
We explore $T \overline T$ deformations of Warped Conformal Field Theories (WCFTs) in two dimensions as examples of $T\overline T$ deformed non-relativistic quantum field theories. WCFTs are quantum field theories with a…
Irregular conformal block is a new tool to study Argyres-Douglas theory, whose irregular vector is represented as a simultaneous eigenstate of a set of positive Virasoro generators. One way to find the irregular conformal block is to use…
It is shown that the deformed Heisenberg algebra involving the reflection operator R (R-deformed Heisenberg algebra) has finite-dimensional representations which are equivalent to representations of paragrassmann algebra with a special…