Related papers: Intertwinings for Continuum Particle Systems: an A…
In this paper we derive intertwining relations for a broad class of conservative particle systems both in discrete and continuous setting. Using the language of point process theory, we are able to derive a natural framework in which…
We present a theorem which elucidates the connection between self-duality of Markov processes and representation theory of Lie algebras. In particular, we identify sufficient conditions such that the intertwining function between two…
We find all factorized duality functions for a class of interacting particle systems. The functions we recover are self-duality functions for interacting particle systems such as zero-range processes, symmetric inclusion and exclusion…
It is long known that quantum Calogero models feature intertwining operators, which increase or decrease the coupling constant by an integer amount, for any fixed number of particles. We name these as ``horizontal'' and construct new…
Duality transformations reveal unexpected equivalences between seemingly distinct models. We introduce an out-of-equilibrium generalisation of matrix product operators to implement duality transformations in one-dimensional boundary-driven…
There is a commutative algebra of differential-difference operators, with two parameters, associated to any dihedral group with an even number of reflections. The intertwining operator relates this algebra to the algebra of partial…
We use linear algebraic methods to obtain general results about linear operators on a space of polynomials that we apply to the operators associated with a polynomial sequence by the monomiality property. We show that all such operators are…
Using a formulation of quantum mechanics based on orthogonal polynomials in the energy and physical parameters, we study quantum systems totally confined in space and associated with the discrete Meixner polynomials. We present several…
The technique of differential intertwining operators (or Darboux transformation operators) is systematically applied to the one-dimensional Dirac equation. The following aspects are investigated: factorization of a polynomial of Dirac…
The aim of this paper is twofold. First, we introduce a new class of linearizations, based on the generalization of a construction used in polynomial algebra to find the zeros of a system of (scalar) polynomial equations. We show that one…
We consider the extension of the Heisenberg vertex operator algebra by all its irreducible modules. We give an elementary construction for the intertwining vertex operators and show that they satisfy a complex parametrized generalized…
We present an algebraic study of a kind of quantum systems belonging to a family of superintegrable Hamiltonian systems in terms of shape-invariant intertwinig operators, that span pairs of Lie algebras like $(su(n),so(2n))$ or…
For a series of Markov processes we prove stochastic duality relations with duality functions given by orthogonal polynomials. This means that expectations with respect to the original process (which evolves the variable of the orthogonal…
We study self-duality for interacting particle systems, where the particles move as continuous time random walkers having either exclusion interaction or inclusion interaction. We show that orthogonal self-dualities arise from unitary…
An algebraic interpretation of the $q$-Meixner polynomials is obtained. It is based on representations of $\mathcal{U}_q(\mathfrak{su}(1,1))$ on $q$-oscillator states with the polynomials appearing as matrix elements of unitary…
The problem of a differential operator left- and right division is solved in terms of generalized Bell polinomials for nonabelian differential unitary ring. The definition of the polinomials is made by means of recurrent relations. The…
We derive raising and lowering operators for orthogonal polynomials on the unit circle and find second order differential and $q$-difference equations for these polynomials. A general functional equation is found which allows one to relate…
We consider two particles performing continuous-time nearest neighbor random walk on $\mathbb Z$ and interacting with each other when they are at neighboring positions. Typical examples are two particles in the partial exclusion process or…
Starting from space-discretisation of Maxwell's equations, various classical formulations are proposed for the simulation of electromagnetic fields. They differ in the phenomena considered as well as in the variables chosen for…
We obtain stochastic duality functions for specific Markov processes using representation theory of Lie algebras. The duality functions come from the kernel of a unitary intertwiner between $*$-representations, which provides (generalized)…