Related papers: pq-Duality: a set of simple examples
The concept of cyclic tridiagonal pairs is introduced, and explicit examples are given. For a fairly general class of cyclic tridiagonal pairs with cyclicity N, we associate a pair of `divided polynomials'. The properties of this pair…
We identify conditions under which a summation over nucleon resonances can yield, via quark-hadron duality, parton model results for electromagnetic and neutrino structure functions at large x. While a summation over the lowest even and odd…
Some aspects of two-dimensional gravity coupled to matter fields, especially to the Sine-Gordon-model are examined. General properties and boundary conditions of possible soliton-solutions are considered. Analytic soliton-solutions are…
An overview of Hamiltonian systems with noncanonical Poisson structures is given. Examples of bi-Hamiltonian ode's, pde's and lattice equations are presented. Numerical integrators using generating functions, Hamiltonian splitting,…
We construct a double degenerate supersymmetry in one dimensional quantum mechanics. Here the energy levels satisfy the conditions $E_{0,1}^{((-)}=0$ and $E_{n,n+1}^{(+)}=E_{n+2,n+3}^{(-)}$.The corresponding SUSY Hamiltonians$(H^{(\pm)}$)…
The Gauss decomposition of quantum groups and supergroups are considered. The main attention is paid to the R-matrix formulation of the Gauss decomposition and its properties as well as its relation to the contraction procedure. Duality…
The approach to the dynamics of a charged particle in the Born-Infeld nonlinear electrodynamics developed in [Phys. Lett. A 240 (1998) 8] is generalized to include a Born-Infeld dyon. Both Hamiltonian and Lagrangian structures of many dyons…
In the two-Higgs-doublet model, different Higgs doublets can be viewed as components of a generic "hyperspinor". We decompose the Higgs potential of this model into irreducible representations of the SU(2) group of transformations of this…
We develop a method to determine the eigenvalues and eigenfunctions of two-boson Hamiltonians include a wide class of quantum optical models. The quantum Hamiltonians have been transformed in the form of the one variable differential…
We develop a theory of two-parameter quantum polynomial functors. Similar to how (strict) polynomial functors give a new interpretation of polynomial representations of the general linear groups $\operatorname{GL}_n$, the two-parameter…
Besides its usual interpretation as a system of $n$ indistinguishable particles moving on the circle, the trigonometric Sutherland system can be viewed alternatively as a system of distinguishable particles on the circle or on the line, and…
It is demonstrated that quasi-exactly solvable models of quantum mechanics admit an interesting duality transformation which changes the form of their potentials and inverts the sign of all the exactly calculable energy levels. This…
For any causal nonlinear electrodynamics theory that is "self-dual" (electromagnetic $U(1)$-duality invariant), the Legendre-dual pair of Lagrangian and Hamiltonian densities $\{\mathcal{L},\mathcal{H}\}$ are constructed from functions…
Let p be an odd prime number and let S be a finite set of prime numbers congruent to 1 modulo p. We prove that the group G_S(Q)(p) has cohomological dimension 2 if the linking diagram attached to S and p satisfies a certain technical…
We consider perturbations in the fields of the 't Hooft-Polyakov monopole, dyon and point electric solutions. We find a series of bound modes where the fields are confined to the core of the respective solutions, and these are interpreted…
The exact solvability of several nuclear models with non-degenerate single-particle energies is outlined and leads to a generalization of integrable Richardson-Gaudin models, like the $su(2)$-based fermion pairing, to any simple Lie…
Let $ G^\tau $ be a connected simply connected semisimple algebraic group, endowed with generalized Sklyanin-Drinfel'd structure of Poisson group, let $ H^\tau $ be its dual Poisson group. By means of quantum double construction and…
We present a summary of the applications of duality to Donaldson-Witten theory and its generalizations. Special emphasis is made on the computation of Donaldson invariants in terms of Seiberg-Witten invariants using recent results in N=2…
Within the framework of Relativistic Schroedinger Theory (an alternative form of quantum mechanics for relativistic many-particle systems) it is shown that a general N-particle system must occur in one of two forms: either as a ``positive''…
The self-dual systems are constrained and so are simpler to understand. In recent years there have been several studies on the self-dual Chern-Simons systems. Here I present a brief survey of works done by my collaborators and myself. I…