Related papers: Spin $q$-Whittaker polynomials
We investigate polynomials, called m-polynomials, whose generator polynomial has coefficients that can be arranged as a matrix, where q is a positive integer greater than one. Orthogonality relations are established and coefficients are…
The fundamental objective of this paper is to obtain some interesting properties for $\left(h,q\right)$-Genocchi numbers and polynomials by using the fermionic $p$-adic $q$-integral on $\mathbb{Z}_{p}$ and mentioned in the paper…
We construct a non-polynomial generalization of the $q$-Askey scheme. Whereas the elements of the $q$-Askey scheme are given by $q$-hypergeometric series, the elements of the non-polynomial scheme are given by contour integrals, whose…
Using the vertex operator representations for symplectic and orthogonal Schur functions, we define two families of symmetric functions and show thatthey are the skew symplectic and skew orthogonal Schur polynomials defined implicitly by…
In this paper, we study some symmetric properties of the multiple q-Euler zeta function. From these properties, we derive several identities of symmetry for the (h;q)-extension of higher-order Euler polynomials.
The Gaussian polynomial in variable $q$ is defined as the $q$-analog of the binomial coefficient. In addition to remarkable implications of these polynomials to abstract algebra, matrix theory and quantum computing, there is also a…
Shifting by \pm 1 powers sums: p_i \to p_i \pm 1 induces a transformation on symmetric functions that we detail in the case of Hall-Littlewood polynomials. By iteration, this gives a description of these polynomials in terms of plane…
Let G be a semi-simple simply connected group over complex numbers. In this paper we give a geometric definition of the (dual) Weyl modules over the group G[t] and show that their characters form an eigen-function of the lattice version of…
We construct a lift of Schur's Q-functions to the peak algebra of the symmetric group, called the noncommutative Schur Q-functions, and extract from them a new natural basis with several nice properties such as the positive right-Pieri…
The aim of the present study is to establish some properties for q-Bessel matrix polynomials such as several q-differential matrix equation, q-differential matrix relations and q-recurrence matrix relations, and integral representation,…
In this work we investigate Plancherel-Rotach type asymptotics for some $q$-series as $q\to1$. These $q$-series generalize Ramanujan function $A_{q}(z)$; Jackson's $q$-Bessel function $J_{\nu}^{(2)}$(z;q), Ismail-Masson orthogonal…
It is well known that the classical families of orthogonal polynomials are characterized as eigenfunctions of a second order linear differential/difference operator. In this paper we present a study of classical orthogonal polynomials in a…
We provide a combinatorial description of the coefficients appearing in the expansion of Hall-Littlewood polynomials in terms of monomial symmetric functions. We also give a Littlewood-Richardson rule for Hall-Littlewood polynomials. For…
We introduce a new family of symmetric multivariate polynomials, whose coefficients are meromorphic functions of two parameters $(q,t)$ and polynomial in a further two parameters $(u,v)$. We evaluate these polynomials explicitly as a matrix…
The Al-Salam-Chihara polynomials are an important family of orthogonal polynomials in one variable $x$ depending on 3 parameters $\alpha$, $\beta$ and $q$. They are closely connected to a model from statistical mechanics called the…
In this paper we aim to specify some characteristics of the so called family of $q$-Appell Polynomials by using $q$-Umbral calculus. Next in our study, we focus on $q$-Genocchi numbers and polynomials as a famous member of this family. To…
This work highlights the existence of partial symmetries in large families of iterated plethystic coefficients. The plethystic coefficients involved come from the expansion in the Schur basis of iterated plethysms of Schur functions indexed…
We study on Weyl modules of cyclotomic $q$-Schur algebras. In particular, we give the character formula of the Weyl modules by using the Kostka numbers and some numbers which are computed by a generalization of Littlewood-Richardson rule.…
We review properties of q-orthogonal polynomials, related to their orthogonality, duality and connection with the theory of symmetric (self-adjoint) operators, represented by a Jacobi matrix. In particular, we show how one can naturally…
We give explicit upper bounds for coefficients of polynomials appearing in Gauss-Kra\"{i}tchik formula for cyclotomic polynomials. We use a certain relation between elementary symmetric polynomials and power sums polynomials.