224 citations · 2.5k across the 74 of their papers we have counts for
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Heisenberg Algebra, Umbral Calculus and Orthogonal Polynomials
G. Dattoli, D. Levi, P. Winternitz
Umbral calculus can be viewed as an abstract theory of the Heisenberg commutation relation . In ordinary quantum mechanics is the derivative and $\hat M…
Superintegrable Systems with a Third Order Integrals of Motion
Ian Marquette, Pavel Winternitz
Two-dimensional superintegrable systems with one third order and one lower order integral of motion are reviewed. The fact that Hamiltonian systems with higher order integrals of m…
Solvable Lie algebras with triangular nilradicals
Sébastien Tremblay, Pavel Winternitz
All finite-dimensional indecomposable solvable Lie algebras , having the triangular algebra T(n) as their nilradical, are constructed. The number of nonnilpotent elements $…
Lie symmetries of multidimensional difference equations
Decio Levi, Sébastien Tremblay, Pavel Winternitz
A method is presented for calculating the Lie point symmetries of a scalar difference equation on a two-dimensional lattice. The symmetry transformations act on the equations and o…
Invariants of the nilpotent and solvable triangular Lie algebras
Sébastien Tremblay, Pavel Winternitz
Invariants of the coadjoint representation of two classes of Lie algebras are calculated. The first class consists of the nilpotent Lie algebras , isomorphic to the algebras…
Lie point symmetries of difference equations and lattices
Decio Levi, Sébastien Tremblay, Pavel Winternitz
A method is presented for finding the Lie point symmetry transformations acting simultaneously on difference equations and lattices, while leaving the solution set of the correspon…