Related papers: Hypergroup properties for the deltoid model

There has recently been interest in relating properties of matrices drawn at random from the classical compact groups to statistical characteristics of number-theoretical L-functions. One example is the relationship conjectured to hold…

We recently conjectured a set of dualities relating two-dimensional orthogonal gauge theories with $\mathcal{N}=(4,4)$ supersymmetry, analogous to Hori's dualities with $\mathcal{N}=(2,2)$ supersymmetry. Here we provide a quantitative test…

Four families of generalizations of trigonometric functions were recently introduced. In the paper the functions are transformed into four families of orthogonal polynomials depending on two variables. Recurrence relations for construction…

Local properties of families of algebraic subsets $W_g$ in Birkhoff strata $\Sigma_{2g}$ of Gr$^{(2)}$ containing hyperelliptic curves of genus $g$ are studied. It is shown that the tangent spaces $T_g$ for $W_g$ are isomorphic to linear…

Given a field $K$, we investigate which subgroups of the group Aut$\mathbb{A}^2_K$ of polynomial automorphisms of the plane are linear or not. The results are contrasted. The group Aut$\mathbb{A}^2_K$ itself is nonlinear, except if $K$ is…

We introduce a generalization of elliptic 6j-symbols, which can be interpreted as matrix elements for intertwiners between corepresentations of Felder's elliptic quantum group. For special parameter values, they can be expressed in terms of…

Let $G\subset SO(4)$ denote a finite subgroup containing the Heisenberg group. In these notes we classify all these groups, we find the dimension of the spaces of $G$-invariant polynomials and we give equations for the generators whenever…

We compute the periods associated with a special class of hyperplane arrangements. In particular, we exhibit a combinatorial condition on the intersection lattice of a hyperplane arrangement that ensures that its associated periods are…

Orthogonal polynomials are of fundamental importance in many fields of mathematics and science, therefore the study of a particular family is always relevant. In this manuscript, we present a survey of some general results of the Hermite…

Let X be a complex projective K3 surface, and let T(X) be its transcendental lattice; the characteristic polynomials of the isometries of T(X) induced by automorphisms of X are powers of cyclotomic polynomials. Which powers of cyclotomic…

We study the weak asymptotic behavior of the zeros of a family of a certain class of (generalized) hypergeometric polynomials, using the associated hypergeometric differential equation, as the parameters go to infinity. We describe the…

We construct a model for the space of automorphisms of a connected p-compact group in terms of the space of automorphisms of its maximal torus normalizer and its root datum. As a consequence we show that any homomorphism to the outer…

We construct a new family of quasi-solvable and N-fold supersymmetric quantum systems where each Hamiltonian preserves an exceptional polynomial subspace of codimension 2. We show that the family includes as a particular case the recently…

We show that the theory of hyperrings, due to M. Krasner, supplies a perfect framework to understand the algebraic structure of the adele class space of a global field. After promoting F1 to a hyperfield K, we prove that a hyperring of the…

For one-matrix models with polynomial potentials, the explicit relationship between the partition function and the isomonodromic tau function for the 2x2 polynomial differential systems satisfied by the associated orthogonal polynomials is…

We give two examples of algebras of differential operators associated to families of matrix valued orthogonal polynomials arising from representations of SU$(N+1)$. The first one gives a commutative algebra and the second one a…

Let k be a field of characteristic zero. We consider graded subalgebras A of k[x_1,...,x_m]/(x_1^2,...,x_m^2) generated by d linearly independant linear forms. Representations of matroids over k provide a natural description of the…

We equip Ellis and Brundan's version of the odd categorified quantum group for sl(2) with a differential giving it the structure of a graded dg-2-supercategory. The presence of the super grading gives rise to two possible…

A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…

We introduce a new collection of special functions associated to a complex curve of genus 2 similar to Kleinian hyperelliptic $\sigma$-function. These functions are related to weight 2 $\theta$-functions in the same fashion as…