224 citations · 2.5k across the 74 of their papers we have counts for
6 papers · 1 filter
Lorentz and Galilei Invariance on Lattices
Decio Levi, Piergiulio Tempesta, Pavel Winternitz
We show that the algebraic aspects of Lie symmetries and generalized symmetries in nonrelativistic and relativistic quantum mechanics can be preserved in linear lattice theories. T…
Exact Solvability of Superintegrable Systems
Piergiulio Tempesta, Alexander V. Turbiner, Pavel Winternitz
It is shown that all four superintegrable quantum systems on the Euclidean plane possess the same underlying hidden algebra . The gauge-rotated Hamiltonians, as well as thei…
The Conformal Group SU(2,2) and Integrable Systems on a Lorentzian Hyperboloid
M. A. del Olmo, M. A. Rodriguez, P. Winternitz
Eleven different types of "maximally superintegrable" Hamiltonian systems on the real hyperboloid are obtained. All of them correspond to a free…
Hyperspherical Harmonics, Separation of Variables and the Bethe Ansatz
J. Harnad, P. Winternitz
The relation between solutions to Helmholtz's equation on the sphere and the $[{\gr sl}(2)]^n$ Gaudin spin chain is clarified. The joint eigenfuctions of the Laplacian an…
Symmetries of the Kadomstev-Petviashvili Hierarchy
A. Yu. Orlov, P. Winternitz
The relation between the $\widehat{\Sl}(\infty)$ algebra of flows commuting with the KP hierarchy and the Kac-Moody-Virasoro Lie point symmetries of individual equations is establi…
Spherical Functions for the Quantum Group su_q(2)
P. Winternitz, G. Rideau
The representation theory of the quantum group su is used to introduce -analogues of the Wigner rotation matrices, spherical functions, and Legendre polynomials. The meth…