Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
- Centre National de la Recherche ScientifiqueFR2k papers
- University of British ColumbiaCA1.9k papers
- McGill UniversityCA1.9k papers
- University of VictoriaCA1.8k papers
- University of California, Santa CruzUS1.7k papers
- Rutherford Appleton LaboratoryGB1.7k papers
- University of ManchesterGB1.7k papers
- Queen Mary University of LondonGB1.7k papers
- University of PisaIT1.6k papers
- University of EdinburghGB1.6k papers
- University of BirminghamGB1.6k papers
- Heidelberg UniversityDE1.6k papers
18 papers · 2 filters
On E-Discretization of Tori of Compact Simple Lie Groups
Jiří Hrivnák, Jiří Patera
Three types of numerical data are provided for compact simple Lie groups of classical types and of any rank. This data is indispensable for Fourier-like expansions of multidime…
New recursive residue formulas for the topological expansion of the Cauchy Matrix Model
Aleix Prats Ferrer
In a recent work [1] we consider the topological expansion for the non-mixed observables (including the free energy) for the formal Cauchy matrix model. The only restriction in [1]…
Two dimensional symmetric and antisymmetric generalizations of sine functions
Jiří Hrivnák, Lenka Motlochová, Jiří Patera
Properties of 2-dimensional generalizations of sine functions that are symmetric or antisymmetric with respect to permutation of their two variables are described. It is shown that…
Two-dimensional symmetric and antisymmetric generalizations of exponential and cosine functions
Jiří Hrivnák, Jiří Patera
Properties of the four families of recently introduced special functions of two real variables, denoted here by , and , are studied. The superscripts and …
Invariant recurrence relations for CP^(N-1) models
P. Goldstein, A. M. Grundland
In this paper, we present invariant recurrence relations for the completely integrable CP^(N-1) Euclidean sigma model in two dimensions defined on the Riemann sphere S^2 when its a…
Periodic orbits for an infinite family of classical superintegrable systems
Frédérick Tremblay, Alexander V. Turbiner, Pavel Winternitz
We show that all bounded trajectories in the two dimensional classical system with the potential $V(r,ϕ)=ω^2 r^2+ \frac{\al k^2}{r^2 \cos^2 {k ϕ}}+ \frac{βk^2}{r^2 \sin^2 {k ϕ}}$ a…
Branching rules for the Weyl group orbits of the Lie algebra A(n)
M. Larouche, M. Nesterenko, J. Patera
The orbits of Weyl groups W(A(n)) of simple A(n) type Lie algebras are reduced to the union of orbits of the Weyl groups of maximal reductive subalgebras of A(n). Matrices transfor…
Superintegrability and higher order polynomial algebras I
Ian Marquette
We present a method to obtain higher order integrals and polynomial algebras for two-dimensional superintegrable systems from creation and annihilation operators. All potentials wi…
Supersymmetry as a method of obtaining new superintegrable systems with higher order integrals of motion
Ian Marquette
The main result of this article is that we show that from supersymmetry we can generate new superintegrable Hamiltonians. We consider a particular case with a third order integral…
Symmetry reduction and superintegrable Hamiltonian systems
M. A. Rodriguez, P. Tempesta, P. Winternitz
We construct complete sets of invariant quantities that are integrals of motion for two Hamiltonian systems obtained through a reduction procedure, thus proving that these systems…
Invariant difference schemes and their application to invariant ordinary differential equations
R. Rebelo, P. Winternitz
We present an exposition of a method of discretizing ordinary differential equations while preserving their Lie point symmetries. This method is very general and can be applied to…
Integrable and superintegrable systems with spin in three-dimensional Euclidean space
P. Winternitz, I. Yurdusen
A systematic search for superintegrable quantum Hamiltonians describing the interaction between two particles with spin 0 and 1/2, is performed. We restrict to integrals of motion…
On Discretization of Tori of Compact Simple Lie Groups
Jiri Hrivnak, Jiri Patera
Three types of numerical data are provided for simple Lie groups of any type and rank. This data is indispensable for Fourier-like expansions of multidimensional digital data into…
An infinite family of solvable and integrable quantum systems on a plane
Frédérick Tremblay, Alexander V. Turbiner, Pavel Winternitz
An infinite family of exactly-solvable and integrable potentials on a plane is introduced. It is shown that all already known rational potentials with the above properties allowing…
Cauchy Biorthogonal Polynomials
M. Bertola, M. Gekhtman, J. Szmigielski
The paper investigates the properties of certain biorthogonal polynomials appearing in a specific simultaneous Hermite-Pade' approximation scheme. Associated to any totally positiv…
Mesoscopic colonization of a spectral band
M. Bertola, S. Y. Lee, M. Y. Mo
We consider the unitary matrix model in the limit where the size of the matrices become infinite and in the critical situation when a new spectral band is about to emerge. In previ…
Topological Expansion for the Cauchy two-Matrix-Model
Marco Bertola, Aleix Prats Ferrer
Recently, a two-matrix-model with a new type of interaction [1] has been introduced and analyzed using bi-orthogonal polynomial techniques. Here we present the complete 1/N^2 expan…
Convolution symmetries of integrable hierarchies, matrix models and τ-functions
J. Harnad, A. Yu. Orlov
Generalized convolution symmetries of integrable hierarchies of KP and 2KP-Toda type multiply the Fourier coefficients of the elements of the Hilbert space $\HH= L^2(S^1)$ by a spe…