91 citations · 1.2k across the 114 of their papers we have counts for
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Algebraic (super-)integrability from commutants of subalgebras in universal enveloping algebras
Rutwig Campoamor-Stursberg, Danilo Latini, Ian Marquette +1
Starting from a purely algebraic procedure based on the commutant of a subalgebra in the universal enveloping algebra of a given Lie algebra, the notion of algebraic Hamiltonians a…
Recurrence relations and general solution of the exceptional Hermite equation
Alfred Michel Grundland, Danilo Latini, Ian Marquette
Exceptional orthogonal Hermite and Laguerre polynomials have been linked to the k-step extension of harmonic and singular oscillators. The exceptional polynomials allow the existen…
Decomposition of enveloping algebras of simple Lie algebras and their related polynomial algebras
Rutwig Campoamor-Stursberg, Ian Marquette
The decomposition problem of the enveloping algebra of a simple Lie algebra is reconsidered combining both the analytical and the algebraic approach, showing its relation with the…
Construction of polynomial algebras from intermediate Casimir invariants of Lie algebras
Danilo Latini, Ian Marquette, Yao-Zhong Zhang
We propose a systematic procedure to construct polynomial algebras from intermediate Casimir invariants arising from (semisimple or non-semisimple) Lie algebras . In…
Generalized quadratic commutator algebras of PBW-type
Ian Marquette, Luke Yates, Peter Jarvis
In recent years, various nonlinear algebraic structures have been obtained in the context of quantum systems as symmetry algebras, Painlevé transcendent models and missing label pr…
Dynamical symmetry algebra of two superintegrable two-dimensional systems
Ian Marquette, Christiane Quesne
A complete classification of 2D superintegrable systems on two-dimensional conformally flat spaces has been performed over the years and 58 models, divided into 12 equivalence clas…