Related papers: Up- and Down-Operators on Young's Lattice
Young's lattice is a prototypical example of differential posets. Differential posets have the Robinson correspondence, the correspondence between permutations and pairs of standard tableaux with the same shape, as in the case of Young's…
In a recent paper a pair of operators $a$ and $b$ satisfying the equations $a^\dagger a=bb^\dagger+\gamma\1$ and $aa^\dagger=b^\dagger b+\delta\1$, has been considered, and their nature of ladder operators has been deduced and analysed.…
A shape invariant nonseparable and nondiagonalizable two-dimensional model with quadratic complex interaction, first studied by Cannata, Ioffe, and Nishnianidze, is re-examined with the purpose of exhibiting its hidden algebraic structure.…
Let $D$ and $U$ be linear operators in a vector space (or more generally, elements of an associative algebra with a unit). We establish binomial-type identities for $D$ and $U$ assuming that either their commutator $[D,U]$ or the second…
In this article the anomalous dimension of a class of operators with a bare dimension of O(N) is studied. The operators considered are dual to excited states of a two giant graviton system. In the Yang Mills theory they are described by…
We present a formulas to add a row or a column to the power, monomial, forgotten, Schur, homogeneous and elementary symmetric functions. As an application of these operators we show that the operator that adds a column to the Schur…
It is known for linear operators with polynomial coefficients annihilating a given D-finite function that there is a trade-off between order and degree. Raising the order may give room for lowering the degree. The relationship between order…
We show that for general deformations of SU(2) algebra, the dynamics in terms of ladder operators is preserved. This is done for a system of precessing magnetic dipole in magnetic field, using the unitary phase operator which arises in the…
Ladder operators are useful, if not essential, in the analysis of some given physical system since they can be used to find easily eigenvalues and eigenvectors of its Hamiltonian. In this paper we extend our previous results on abstract…
A class of algebras called down-up algebras was introduced by G. Benkart and T. Roby. We classify the finite dimensional simple modules over Noetherian down-up algebras and show that in some cases every finite dimensional module is…
In this paper we describe two pairs of raising/lowering operators for Askey-Wilson polynomials, which result from constructions involving very different techniques. The first technique is quite elementary, and depends only on the…
We find the raising and lowering operators for orthogonal polynomials on the unit circle introduced by Szeg\H{o} and for their four parameter generalization to ${}_4\phi_3$ biorthogonal rational functions on the unit circle.
This paper deals with decreasing operators on back stable Schubert polynomials. We study two operators $\xi$ and $\nabla$ of degree $-1$, which satisfy the Leibniz rule. Furthermore, we show that all other such operators are linear…
A generalised ladder operator is used to construct the conserved operators for any model derived from the Yang-Baxter equation. As an example, the low order conserved operators for the XYh model are calculated explicitly.
We establish a correspondence between Young diagrams and differential operators of infinitely many variables. These operators form a commutative associative algebra isomorphic to the algebra of the conjugated classes of finite permutations…
Under some hypotheses (symmetry, confluence), we enumerate all quadratically presented algebras, generated by creation and destruction operators, in which number operators exist. We show that these are algebras of bosons, fermions, their…
We present, for the isospectral family of oscillator Hamiltonians, a systematic procedure for constructing raising and lowering operators satisfying any prescribed `distorted' Heisenberg algebra (including the $q$-generalization). This is…
While studying some properties of linear operators in a Euclidean Jordan algebra, Gowda, Sznajder and Tao have introduced generalized lattice operations based on the projection onto the cone of squares. In two recent papers of the authors…
We apply the Schr\"odinger factorization to construct the ladder operators for hydrogen atom, Mie-type potential, harmonic oscillator and pseudo-harmonic oscillator in arbitrary dimensions. By generalizing these operators we show that the…
The Leibniz bracket of an operator on a (graded) algebra is defined and some of its properties are studied. A basic theorem relating the Leibniz bracket of the commutator of two operators to the Leibniz bracket of them, is obtained. Under…