Related papers: Orthogonal polynomials and the deformed Jordan pla…
We describe poles and the corresponding residual automorphic representations of Eisenstein series attached to maximal parabolic subgroups whose unipotent radicals admit Jordan algebra structure.
We show that the symmetry operators for the quantum superintegrable system on the 3-sphere with generic 4-parameter potential form a closed quadratic algebra with 6 linearly independent generators that closes at order 6 (as differential…
The relation between Wilson and para-Racah polynomials and representations of the degenerate rational Sklyanin algebra is established. Second order Heun operators on quadratic grids with no diagonal terms are determined. These special or…
Let $X$ and $Y$ be Banach spaces, let $\mathcal{A}(X)$ stands for the algebra of approximable operators on $X$, and let $P\colon\mathcal{A}(X)\to Y$ be an orthogonally additive, continuous $n$-homogeneous polynomial. If $X^*$ has the…
We give a complete description of the finite-dimensional irreducible representations of the Yangian associated with the orthosymplectic Lie superalgebra $\frak{osp}_{1|2}$. The representations are parameterized by monic polynomials in one…
Let $\mathcal{H}$ be a complex Hilbert space, $\mathcal{B(H)}$ be the algebra of all bounded linear operators on $\mathcal{H}$ and $\mathcal{A} \subseteq \mathcal{B(H)}$ be a von Neumann algebra without central summands of type $I_1$. For…
Let $A$ and $B$ be associative algebras over a field $F$ with {\rm char}$(F)\ne 2$. Our first main result states that if $A$ is unital and equal to its commutator ideal, then every Jordan epimorphism $\varphi:A\to B$ is the sum of a…
A noncommutative Jordan algebra of a specific type is attached to any (-1,-1)-balanced Freudenthal Kantor triple system, in such a way that the triple product in this system is determined by the binary product in the algebra. Over fields of…
In this article a complete description is given of the simple representations of a 3-dimensional Sklyanin algebra associated to a torsion point. In order to determine these irreducible representations, a review is given of classical results…
The tridiagonal algebra is defined by two generators and two relations, called the tridiagonal relations. Special cases of the tridiagonal algebra include the $q$-Onsager algebra, the positive part of the $q$-deformed enveloping algebra…
Moduli spaces of Abelian and quadratic differentials are stratified by multiplicities of zeroes; connected components of the strata correspond to ergodic components of the Teichmuller geodesic flow. It is known that the strata are not…
We identify the Atkin polynomials in terms of associated Jacobi polynomials. Our identificationthen takes advantage of the theory of orthogonal polynomials and their asymptotics to establish many new properties of the Atkin polynomials.…
Let A be an associative complex algebra and L an invariant linear functional on it (trace). Let i be an involutive antiautomorphism of A such that L(i(a))=L(a) for any a in A. Then A admits a symmetric invariant bilinear form (a, b)=L(a…
Operators that intertwine representations of a degenerate version of the double affine Hecke algebra are introduced. Each of the representations is related to multi-variable orthogonal polynomials associated with Calogero-Sutherland type…
New differential-recurrence properties of dual Bernstein polynomials are given which follow from relations between dual Bernstein and orthogonal Hahn and Jacobi polynomials. Using these results, a fourth-order differential equation…
For every multivariable polynomial $p$, with $p(0)=1$, we construct a determinantal representation $$p=\det (I - K Z),$$ where $Z$ is a diagonal matrix with coordinate variables on the diagonal and $K$ is a complex square matrix. Such a…
The two-body Coulomb Hamiltonian, when calculated in Coulomb-Sturmian basis, has an infinite symmetric tridiagonal form, also known as Jacobi matrix form. This Jacobi matrix structure involves a continued fraction representation for the…
In the article we study the simple unital communitative three-dimensional algebras over an algebraically closed field of characteristic not equal to 2. It is proved that every simple unital communitative three-dimensional algebra of…
We construct generators of the center of the universal enveloping algebra of the complex orthogonal Lie algebra realized as the alternative matrices of size $n$. These elements are constructed in accordance with the Iwasawa decomposition of…
In this paper, we obtain analogues of Jacobi's derivative formula in terms of the theta constants with rational characteristics. For this purpose, we use the arithmetic formulas of the number of representations of a natural number…