Related papers: A remark on the q-hypergeometric integral Bailey p…
We study solutions of the reflection equation related to the quantum affine algebra $U_q(\widehat{sl_n})$. First, we explain how to construct a family of stochastic integrable vertex models with fixed boundary conditions. Then, we construct…
Generalized integral formulas involving the generalized Bessel-Maitland function are considered and it expressed in terms of generalized Wright hypergeometric functions. By assuming appropriate values of the parameters in the main results,…
The (G, \theta)-Lie algebras are structures which unify the Lie algebras and Lie superalgebras. We use them to produce solutions for the quantum Yang-Baxter equation. The constant and the spectral-parameter Yang-Baxter equations and…
We examine the convergence of $q$-hypergeometric series when $|q|=1$.
Star configurations are certain unions of linear subspaces of projective space. They have appeared in several different contexts: the study of extremal Hilbert functions for fat point schemes in the plane; the study of secant varieties of…
We offer a more general Bailey pair than one that was proved in two different papers by two different methods [5, 12].
We show that the eigenvalues and eigenfunctions of the stargenvalue equation can be completely expressed in terms of the corresponding eigenvalue problem for the quantum Hamiltonian. Our method makes use of a Weyl-type representation of the…
We give a connection formula for the Jackson integral of Riemann-Papperitz type. This includes a solution of the connection problem for the variant of $q$-hypergeometric equation of degree three introduced by Hatano-Matsunawa-Sato-Takemura.…
Versions of Bailey's lemma which change the base from q to q^2 or q^3 are given. Iterates of these versions give many new versions of multisum Rogers-Ramanujan identities. We also prove Melzer's conjectures for the Fermionic forms of the…
The univariate elliptic beta integral is represented as a bilinear combination of infinite $_{10}V_9$ very-well-poised elliptic hypergeometric series representing the sum of residues of the integrand poles. Convergence of this combination…
We construct the new q-extension of Bernoulli numbers and polynomials in this paper. Finally we consider the q-zeta functions which interpolate the new q-extension of Bernoulli numbers and polynomials.
We construct a family of measures on flag spaces (or, equivalently, on the spaces of upper-triangular matrices) compatible with respect to natural projections. We obtain an $n(n-1)/2$-parametric family of beta-integrals over space of…
With the help of the partial derivative operator and several summation formulas for hypergeometric series, we find three double series for $\pi$. In terms of the operator just stated and several summation formulas for basic hypergeometric…
We present a multi-spin solution to the Yang-Baxter equation. The solution corresponds to the integrable lattice spin model of statistical mechanics with positive Boltzmann weights and parameterized in terms of the basic hypergeometric…
Maximal $(k+1)$-crossing-free graphs on a planar point set in convex position, that is, $k$-triangulations, have received attention in recent literature, with motivation coming from several interpretations of them. We introduce a new way of…
We introduce a bilateral extension of the continuous $q$-ultraspherical polynomials which we call bilateral $q$-ultraspherical functions. These functions are given as specific bilateral basic hypergeometric ${}_2\psi_2$ series, they are…
In this paper we offer some new identities associated with mock theta functions and establish new Bailey pairs related to indefinite quadratic forms. We believe our proof is instructive use of changing base of Bailey pairs, and offers new…
In this paper, we investigate a number of $q$-supercongruences on double and triple sums. By means of a lemma devised by El Bachraoui and its generalization, we transform some $q$-supercongruences on double and triple sums into the…
We generalize the result of the preceeding paper and solve the Yang-Baxter equation in terms of triple systems called orthogonal and symplectic ternary systems. In this way, we found several other new solutions.
Higher-point functions of gauge invariant composite operators in N=4 super Yang-Mills theory can be computed via triangulation. The elementary tile in this process is the hexagon introduced for the evaluation of structure constants. A…