Related papers: Deformed Dolan-Grady relations in quantum integrab…
We develop our method to prove quantum superintegrability of an integrable 2D system, based on recurrence relations obeyed by the eigenfunctions of the system with respect to separable coordinates. We show that the method provides rigorous…
An N-dimensional position-dependent mass Hamiltonian (depending on a parameter \lambda) formed by a curved kinetic term and an intrinsic oscillator potential is considered. It is shown that such a Hamiltonian is exactly solvable for any…
By using a class of `anyon like' representations of permutation algebra, which pick up nontrivial phase factors while interchanging the spins of two lattice sites, we construct some integrable variants of $SU(M)$ Haldane-Shastry (HS) spin…
For nonrelativistic Hamiltonians which are shape invariant, analytic expressions for the eigenvalues and eigenvectors can be derived using the well known method of supersymmetric quantum mechanics. Most of these Hamiltonians also possess…
We consider integrable vertex models whose Boltzmann weights (R-matrices) are trigonometric solutions to the graded Yang-Baxter equation. As is well known the latter can be generically constructed from quantum affine superalgebras…
The recent construction of integrable quantum field theories on two-dimensional Minkowski space by operator-algebraic methods is extended to models with a richer particle spectrum, including finitely many massive particle species…
Recent progress in quantum field theory and quantum gravity relies on mixed boundary conditions involving both normal and tangential derivatives of the quantized field. In particular, the occurrence of tangential derivatives in the boundary…
Various applications of quantum algebraic techniques in nuclear structure physics, such as the su$_q$(2) rotator model and its extensions, the use of deformed bosons in the description of pairing correlations, and the construction of…
Quantum algebras (also called quantum groups) are deformed versions of the usual Lie algebras, to which they reduce when the deformation parameter q is set equal to unity. From the mathematical point of view they are Hopf algebras. Their…
Recently, we presented a new class of quantum-mechanical Hamiltonians which can be written as the $F^{th}$ power of a conserved charge: $H=Q^F$ with $F=2,3,...\,.$ This construction, called fractional supersymmetric quantum mechanics, was…
Quantum integrable models that possess $N=2$ supersymmetry are investigated on the half-space. Conformal perturbation theory is used to identify some $N=2$ supersymmetric boundary integrable models, and the effective boundary…
Upon introducing a one-parameter quadratic deformation of the q-boson algebra and a diagonal perturbation at the end point, we arrive at a semi-infinite q-boson system with a two-parameter boundary interaction. The eigenfunctions are shown…
A special class of integrable nonlinear differential equations related to A.III-type symmetric spaces and having additional reductions are analyzed via the inverse scattering method (ISM). Using the dressing method we construct two classes…
The Yang-Baxter $\sigma$-model is an integrable deformation of the principal chiral model on a Lie group $G$. The deformation breaks the $G \times G$ symmetry to $U(1)^{\textrm{rank}(G)} \times G$. It is known that there exist non-local…
Let $\C$ denote the field of complex numbers, and fix a nonzero $q \in \C$ such that $q^4 \ne 1$. Define a $\C$-algebra $\Delta_q$ by generators and relations in the following way. The generators are $A,B,C$. The relations assert that each…
Let $\mathcal{V}^c(\mathfrak{gl}_N)$ be Etingof--Kazhdan's quantum affine vertex algebra associated with the trigonometric $R$-matrix. We establish a connection between suitably generalized deformed $\phi$-coordinated…
A global model of $q$-deformation for the quasi--orthogonal Lie algebras generating the groups of motions of the four--dimensional affine Cayley--Klein geometries is obtained starting from the three dimensional deformations. It is shown how…
Quantum algebras are a mathematical tool which provides us with a class of symmetries wider than that of Lie algebras, which are contained in the former as a special case. After a self-contained introduction to the necessary mathematical…
A $\gamma$-deformed version of $\mathfrak{su}(2)$ algebra has been obtained from a bi-orthogonal system of vectors in $\bf{C^2}$. Fusion of Jordan-Schwinger realization of complexified $\mathfrak{su}(2)$ with Dyson-Maleev representation…
Fractional supersymmetric quantum mechanics of order $\lambda$ is realized in terms of the generators of a generalized deformed oscillator algebra and a Z$_{\lambda}$-grading structure is imposed on the Fock space of the latter. This…