Related papers: Factorized $A_2$-Leonard pair

The natural representation of the quantized affine algebra of type A can be defined via the deformed Fock space by Misra and Miwa. This relates the classes of Weyl modules for a type A quantum group at a root of unity to the action of the…

In this paper new classes of $L_2$-orthogonal functions are constructed as iterated $L_2$-orthogonal systems. In order to do this we use the theory of the Riemann's zeta-function as well as our theory of Jacob's ladders. The main result is…

Fix an algebraically closed field $\F$ and an integer $d \geq 3$. Let $V$ be a vector space over $\F$ with dimension $d+1$. A Leonard pair on $V$ is a pair of diagonalizable linear transformations $A: V \to V$ and $A^* : V \to V$, each…

We describe fast algorithms for approximating the connection coefficients between a family of orthogonal polynomials and another family with a polynomially or rationally modified measure. The connection coefficients are computed via…

This paper introduces lax orthogonal algebraic weak factorisation systems on 2-categories and describes a method of constructing them. This method rests in the notion of simple 2-monad, that is a generalisation of the simple reflections…

We investigate tensor products of matrix factorisations. This is most naturally done by formulating matrix factorisations in terms of bimodules instead of modules. If the underlying ring is C[x_1,...,x_N] we show that bimodule matrix…

We classify all pairs of recurrence relations in which two Hahn or dual Hahn polynomials with different parameters appear. Such couples are referred to as (dual) Hahn doubles. The idea and interest comes from an example appearing in a…

In this paper we study factorization formulae for the Lax matrices of the classical Ruijsenaars-Schneider and Calogero-Moser models. We review the already known results and discuss their possible origins. The first origin comes from the…

We define two pairings relating the A-motive with the dual A-motive of an abelian Anderson A-module. We show that specializations of these pairings give the exponential and logarithm functions of this Anderson A-module, and we use these…

We present an algebraic theory of orthogonal polynomials in several variables that includes classical orthogonal polynomials as a special case. Our bottom line is a straightforward connection between apolarity of binary forms and the inner…

A class of one dimensional classical systems is characterized from an algebraic point of view. The Hamiltonians of these systems are factorized in terms of two functions that together with the Hamiltonian itself close a Poisson algebra.…

This paper demonstrates how to explicitly construct a bidiagonal factorization of the banded recurrence matrix that appears in mixed multiple orthogonality on the step-line in terms of the coeffcients of the mixed multiple orthogonal…

Four families of generalizations of trigonometric functions were recently introduced. In the paper the functions are transformed into four families of orthogonal polynomials depending on two variables. Recurrence relations for construction…

In a recent article with Oleg Smirnov, we defined short Peirce (SP) graded Kantor pairs. For any such pair P, we defined a family, parameterized by the Weyl group of type BC_2, consisting of SP-graded Kantor pairs called Weyl images of P.…

A double category of relations is essentially a cartesian equipment with strong, discrete and functorial tabulators and for which certain local products satisfy a Frobenius Law. A double category of relations is equivalent to a double…

In prior work, the authors, along with M. McClard, R. A. Proctor, and N. J. Wildberger, studied certain distributive lattice models for the `Weyl bialternants' (aka `Weyl characters') associated with the rank two root systems/Weyl groups.…

Unlike in complex linear operator theory, polynomials or, more generally, Laurent series in antilinear operators cannot be modelled with complex analysis. There exists a corresponding function space, though, surfacing in spectral mapping…

To a singular knot K with n double points, one can associate a chord diagram with n chords. A chord diagram can also be understood as a 4-regular graph endowed with an oriented Euler circuit. L. Traldi introduced a polynomial invariant for…

We consider a family of generic weighted arrangements of $n$ hyperplanes in $\C^k$ and show that the Gauss-Manin connection for the associated hypergeometric integrals, the contravariant form on the space of singular vectors, and the…

Let $K$ denote a field and let $V$ denote a vector space over $K$ with finite positive dimension. We consider a pair of linear transformations $A:V\to V$ and $A^*:V\to V$ that satisfy both conditions below: (i) There exists a basis for $V$…