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 Hamiltonians, quadratic supersymmetry, closed extension of transformation operators, chains of transformations, and finally particular cases of pseudoscalar and s...

Level-one representations of the quantum affine superalgebra Uq[ ̂ gl(N |N)] associated to the appropriate non-standard system of simple roots and q-vertex operators (intertwining operators) associated with the level-one modules are constructed explicitly in terms of free bosonic fields. Zhang: Level-One Representations and Vertex Operators of Uq[ ̂ gl(N |N)] 1

Abstract. 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 derivatives. This paper presents an explicit form of the action of the intertwining operator on polynomials by use of harmonic and Jacobi polynomials. The ...

This paper is a continuation of our papers EK1, EK2]. In EK2] we showed that for the root system A n1 one can obtain Macdonald's polynomials { a new interesting class of symmetric functions recently deened by I. Macdonald M1] { as weighted traces of intertwining operators between certain nite-dimensional representations of U q sl n. The main goal of the present paper is to use this construction...

We propose a differential representation for the operators satisfying the q-mutation relation BB† − q B†B = 1 which generalizes a recent result by Eremin and Meldianov, and we discuss in detail this choice in the limit q → 1. Further, we build up non-linear and Gazeau-Klauder coherent states associated to the free quonic hamiltonian h1 = B †B. Finally we construct almost isospectrals quonic ham...

We prove an S3-symmetry of the Jacobi identity for intertwining operator algebras. Since this Jacobi identity involves the braiding and fusing isomorphisms satisfying the genus-zero Moore–Seiberg equations, our proof uses not only the basic properties of intertwining operators, but also the properties of braiding and fusing isomorphisms and the genus-zero Moore–Seiberg equations. Our proof depe...

Three questions about the intertwining operators for the generalized principal series on a symmetric R-space are solved : description of the functional kernel, both in the noncompact and in the compact picture, domain of convergence, meromorphic continuation. A large use is made of the theory of positive Jordan triple systems. The meromorphic continuation of the intertwining integral is achieve...