Related papers: Hyperdeterminants as integrable discrete systems

We study the N=2 four-dimensional superconformal index in various interesting limits, such that only states annihilated by more than one supercharge contribute. Extrapolating from the SU(2) generalized quivers, which have a Lagrangian…

In this article, we discuss about the resolution of the Riemann problem for a 2x2 system in nonconservative form exhibiting parabolic degeneracy. The system can be perceived as the limiting equation (depending on a parameter tending to 0)…

We provide a short proof of the theorem that every real multivariate polynomial has a symmetric determinantal representation, which was first proved in J. W. Helton, S. A. McCullough, and V. Vinnikov, Noncommutative convexity arises from…

Let $M$ be a compact hyperkaehler manifold. The hyperkaehler structure equips $M$ with a set $R$ of complex structures parametrized by $CP^1$, called "the set of induced complex structures". It was known previously that induced complex…

We assign some kind of invariant manifolds to a given integrable PDE (its discrete or semi-discrete variant). First, we linearize the equation around its arbitrary solution $u$. Then we construct a differential (respectively, difference)…

Multidimensional Consistency becomes more and more important in the theory of discrete integrable systems. Recently, we gave a classification of all 3D consistent 6-tuples of equations with the tetrahedron property, where several novel…

We study point and higher symmetries for the hydrodynamic-type systems with two independent variables $t$ and $x$ with and without explicit dependence of the equations on $t,x$. We consider those systems which possess an…

We reconsider non-degenerate second order superintegrable systems in dimension two as geometric structures on conformal surfaces. This extends a formalism developed by the authors, initially introduced for (pseudo-)Riemannian manifolds of…

We extend the Howlett-Isaacs theorem on the solvability of groups of central type taking into account actions by automorphisms. Then we study certain induced characters whose constituents have all the same degree.

We quantify the subcriticality of the bilaplacian in dimensions greater than four by providing explicit repulsivity/smallness conditions on complex additive perturbations under which the spectrum remains stable. Our assumptions cover…

Explicit symplectic integrators have been important tools for accurate and efficient approximations of mechanical systems with separable Hamiltonians. For the first time, the article proposes for arbitrary Hamiltonians similar integrators,…

Let $G$ be a reductive group and $\theta$ an involution on $G$, both defined over a $p$-adic field. We provide a criterion for $G^\theta$-integrability of matrix coefficients of representations of $G$ in terms of their exponents along…

We develop a framework to give upper bounds on the "practical" computational complexity of stability problems for a wide range of nonlinear continuous and hybrid systems. To do so, we describe stability properties of dynamical systems using…

Using geometrical approach exposed in arXiv:math/0304245 and arXiv:nlin/0511012, we explore the Camassa-Holm equation (both in its initial scalar form, and in the form of 2x2-system). We describe Hamiltonian and symplectic structures,…

Together with David Schlang we computed the discriminants of the invariant Hermitian forms for all indicator $o$ even degree absolutely irreducible characters of the ATLAS groups supplementing the tables of orthogonal determinants computed…

Let $A$, $B$ be multidimensional matrices of boundary format respectively $\prod_{i=0}^p(k_i+1)$, $\prod_{j=0}^q(l_j+1)$. Assume that $k_p=l_0$ so that the convolution $A\ast B$ is defined. We prove that $Det (A\ast B)=Det(A)^{\alpha}\cdot…

An important question in dynamical systems is the classification problem, i.e., the ability to distinguish between two isomorphic systems. In this work, we study the topological factors between a family of multidimensional substitutive…

Solutions of the discrete Painlev\'e II hierarchy are shown to be in relation with a family of Toeplitz determinants describing certain quantities in multicritical random partitions models, for which the limiting behavior has been recently…

I show that the basic structure of symplectic integrators is governed by a theorem which states {\it precisely}, how symplectic integrators with positive coefficients cannot be corrected beyond second order. All previous known results can…

This paper treat determinacy of strong moment problems in part I and indeterminacy of strong moment problems in part II. This paper is a summary of the following papers: [1] Ald\'en. E., Determinacy of Strong Moment Problems. [2] On…