Related papers: Fusion procedure for cyclotomic BMW algebras
We introduce the notion of generalized bialgebra, which includes the classical notion of bialgebra (Hopf algebra) and many others. We prove that, under some mild conditions, a connected generalized bialgebra is completely determined by its…
In an isomorphic copy of the ring of symmetric polynomials we study some families of polynomials which are indexed by rational weight vectors. These families include well known symmetric polynomials, such as the elementary, homogeneous, and…
For families of orthogonal and symplectic types quantum matrix (QM-) algebras, we derive corresponding versions of the Cayley-Hamilton theorem. For a wider family of Birman-Murakami-Wenzl type QM-algebras, we investigate a structure of its…
This note contains a short proof of a classical result: any rational symplectic matrix can be put in diagonal form after right and left multiplication by integral symplectic matrices.
H. Widom derived formulae expressing correlation functions of orthogonal and symplectic ensembles of random matrices in terms of orthogonal polynomials (H. Widom. J. Stat. Phys. 94, (1999) 347-363). We obtain similar results for discrete…
We study analogues of Jucys-Murphy elements in cellular algebras arising from repeated Jones basic constructions. Examples include Brauer and BMW algebras and their cyclotomic analogues.
We prove that two finite prime $\Omega$-algebras defined over the same unital commutative ring and satisfying the same set of polynomial identities are isomorphic.
In this paper we consider Idempotent Functional Analysis, an `abstract' version of Idempotent Analysis developed by V. P. Maslov and his collaborators. We give a review of the basic ideas of Idempotent Analysis. The correspondence between…
We give an alternate presentation of the cyclotomic rational Cherednik algebra, which has the useful feature of compatibility with the Opdam-Dunkl subalgebra. This presentation has a diagrammatic flavor, and it provides a simple explanation…
The purpose of this paper is to introduce basic concepts that are fundamental in the examination of composite moduli, while avoiding the notoriously difficult problem of prime-factorization. We introduce a new class of numbers, called…
We give a new operator formula for Grothendieck polynomials that generalizes Magyar's Demazure operator formula for Schubert polynomials. Our proofs are purely combinatorial, contrasting with the geometric and representation theoretic tools…
Let $A$ be a unital $B_{0}$-algebra with an orthogonal basis, then every multiplicative linear functional on $A$ is continuous. This gives an answer to a problem posed by Z. Sawon and Z. Wronski.
For a commutative finite $\mathbb{Z}$-algebra, i.e., for a commutative ring $R$ whose additive group is finitely generated, it is known that the group of units of $R$ is finitely generated, as well. Our main results are algorithms to…
We prove the Box Conjecture for pairs of commuting nilpotent matrices, as formulated by Iarrobino et al [28]. This describes the Jordan type of the dense orbit in the nilpotent commutator of a given nilpotent matrix. Our main tool is the…
To every automorphism w of an infinite rooted regular binary tree we associate a two variable generating function \Phi_w that encodes information on the orbit structure of w. We prove that this is a rational function if w can be described…
When can a primitive of a given algebraic function be con-structed by iteratively solving algebraic equations and composing withthe primitives of some other given algebraic functions or their inverses? We establish some results in this…
An adaptive procedure for constructing polynomials which are biorthogonal to the basis of monomials in the same finite-dimensional inner product space is proposed. By taking advantage of available orthogonal polynomials, the proposed…
We exhibit new biorthogonal sequences generated by index integrals of the squares of the modified Bessel functions and gamma functions. The composition orthogonality, involving differential operators is employed. Generalized Wilson…
A unified algebraic interpretation of both finite families of orthogonal polynomials and biorthogonal rational functions of $q$-Hahn type is provided. The approach relies on the meta $q$-Hahn algebra and its finite-dimensional bidiagonal…
Casimir W-algebras are shown to exist in such a way that the conformal spins of primary(generating) fields coincide with the orders of independent Casimir operators. We show here that this coincidence can be extended further to the case…