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The purpose of this paper is to prove connections among the asymptotic behavior of the magnetization, the structure of the phase transitions, and a class of polynomials that we call the Ginzburg–Landa...
We introduce a family of exactly-solvable two-dimensional Hamiltonians whose wave functions are given in terms of Laguerre and exceptional Jacobi polynomials. The Hamiltonians contain purely quantum t...
Abstract: The explicit formula, which expresses the Alexander polynomials \Delta_{n,3}(t) of torus knots T(n,3) as a sum of the Alexander polynomials \Delta_{k,2}(t) of torus knots T(k,2), is found. U...
Abstract: We show that a large class of bosonic spin-singlet Fractional Quantum Hall model wave-functions and their quasi-hole excitations can be written in terms of Jack polynomials with a prescribed...
Orthogonal polynomials in the normal matrix model with a cubic potential.
Systems of Kowalevski type, discriminantly separable polynomials and quad-graphs.
Abstract: A set of r non-Hermitian oscillator Hamiltonians in r dimensions is shown to be simultaneously diagonalizable. Their spectra is real and the common eigenstates are expressed in terms of mult...
Abstract: We present a simple and fast algorithm for the computation of the coefficients of the expansion of a function f(cos u) in ultraspherical (Gegenbauer) polynomials. We prove that these coeffic...
Abstract: In this article, we are interested in the enumeration of Fully Packed Loops configurations on a grid with a given noncrossing matching. These quantities also appear as the groundstate compon...
Abstract: In this paper we present the generating function method for the derivation of bosons polynomials of Gel'fand basis and Wigner coefficients for the canonical basis of SU(n). We find a new ana...
Higher-order SUSY, exactly solvable potentials, and exceptional orthogonal polynomials.
Abstract: In this paper matrix orthogonal polynomials in the real line are described in terms of a Riemann--Hilbert problem. This approach provides an easy derivation of discrete equations for the cor...
Integrable theory is formulated for correlation functions of characteristic polynomials associated with invariant non-Gaussian ensembles of Hermitean random matrices. By embedding the correlation func...
We present various results on the properties of the four infinite sets of the exceptional $X_{\ell}$ polynomials discovered recently (Odake and Sasaki, Phys. Lett. {\bf B679} (2009) 414-417). These $X...
In this paper, we apply to (almost) all the “named” polynomials of the Askey scheme, as defined by their standard three-term recursion relations, the machinery developed in previous papers. For each o...

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