Related papers: Discrete orthogonal ensemble on the exponential la…

A multi-dimensional bilateral $q$-series extending the $q$-Selberg integral is studied using concepts of truncation, regularization and connection formulae. Following Aomoto's method, which involves regarding the $q$-series as a solution of…

The Al-Salam & Carlitz polynomials are $q$-generalizations of the classical Hermite polynomials. Multivariable generalizations of these polynomials are introduced via a generating function involving a multivariable hypergeometric function…

Let $RG$ be the group ring of a finite group $G$ over a commutative ring $R$ with $1$. An element $x$ in $RG$ is said to be skew-symmetric with respect to an involution $\sigma$ of $RG$ if $\sigma(x)=-x.$ A structure theorem for the…

A representation of the central extension of the unitary Lie algebra coordinated with a skew Laurent polynomial ring is constructed using vertex operators over an integral Z_2-lattice. The irreducible decomposition of the representation is…

We proceed with studying the q-analogues of Cartan domains introduced in q-alg/9703005 and turn to the case of a ball in the space of complex matrices. An explicit expression for a positive $U_q\frak{su}_{nm}$-invariant integral (see…

In this paper, by introducing new matrix operations and using a specific inverse relation, we establish the dual forms of the orthogonality relations for some well-known discrete and continuous $q$-orthogonal polynomials from the…

We study connections between the ring of symmetric functions and the characters of irreducible finite-dimensional representations of quantum affine algebras. We study two families of representations of the symplectic and orthogonal Lie…

We show that several families of classical orthogonal polynomials on the real line are also orthogonal on the interior of an ellipse in the complex plane, subject to a weighted planar Lebesgue measure. In particular these include Gegenbauer…

Using a special case of Askey's $q$-beta integral evaluation formula, we determine orthogonality relations for the Al-Salam--Carlitz polynomials of type II with respect to a family of measures supported on a discrete subset of $\mathbb R$.…

We compute the leading and sub-leading terms in the asymptotic expansion of the Szeg\"o kernel on the diagonal of a class of pseudoconvex Reinhardt domains whose boundaries are endowed with a general class of smooth measures. We do so by…

Let L be a holomorphic line bundle over a compact complex projective Hermitian manifold X. Any fixed smooth hermitian metric h on L induces a Hilbert space structure on the space of global holomorphic sections with values in the k th tensor…

For any skew symmetric matrix over complex numbers, we introduce an EALA and it is called Skew Symmetric Extended Affine Lie Algebra (SSEALA). This way we get a large class of EALAs and most often they are non-isomorphic. In this paper we…

We review properties of the $q-$Hermite polynomials and indicate their links with the Chebyshev, Rogers--Szeg\"{o}, Al-Salam--Chihara, continuous $q-$% utraspherical polynomials. In particular we recall the connection coefficients between…

In this work, we introduce and construct specific $q$-polynomials that are desired from the well-established families of $q$-orthogonal polynomials, namely little $q$-Jacobi polynomials and $q$-Laguerre polynomials, respectively. We examine…

We introduce two explicit examples of polynomials orthogonal on the unit circle. Moments and the reflection coefficients are expressed in terms of Jacobi elliptic functions. We find explicit expression for these polynomials in terms of a…

We consider a reproducing kernel Hilbert space of discrete entire functions on the square lattice $\mathbb Z^2$ inspired by the classical Paley-Wiener space of entire functions of exponential growth in the complex plane. For such space we…

The concept of permutograph is introduced and properties of integral functions on permutographs are established. The central result characterizes the class of integral functions that are representable as lattice polynomials. This result is…

We study quasi-isometric embeddings of symmetric spaces and non-uniform irreducible lattices in semisimple higher rank Lie groups. We show that any quasi-isometric embedding between symmetric spaces of the same rank can be decomposed into a…

We consider discrete orthogonal polynomial ensembles which are discrete analogues of the orthogonal polynomial ensembles in random matrix theory. These ensembles occur in certain problems in combinatorial probability and can be thought of…

In this note, we apply kernel polynomials to find the explicit inverses for some some Hankel matrices associated with q-orthogonal polynomials.