91 citations · 1.2k across the 114 of their papers we have counts for
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Bethe ansatz solutions and hidden algebraic structure for a class of quasi-exactly solvable systems
Siyu Li, Ian Marquette, Yao-Zhong Zhang
The construction of analytic solutions for quasi-exactly solvable systems is an interesting problem. We revisit a class of models for which the odd solutions were largely missed pr…
On polynomial symmetry algebras underlying superintegrable systems in Darboux spaces
Ian Marquette, Junze Zhang, Yao-Zhong Zhang
We review three different approaches to polynomial symmetry algebras underlying superintegrable systems in Darboux spaces. The first method consists of using deformed oscillator al…
Special function models of indecomposable representations: The Laguerre Case
Sébastien Bertrand, Ian Marquette, Willard Miller +1
In this paper, we point out connections between certain types of indecomposable representations of and generalizations of well-known orthogonal polynomials. Those represent…
Superintegrability and Deformed Oscillator Realizations of Quantum TTW Hamiltonians on Constant-Curvature Manifolds and with Reflections in a Plane
Ian Marquette, Anthony Parr
We extend the method for constructing symmetry operators of higher order for two-dimensional quantum Hamiltonians by Kalnins, Kress and Miller (2010). This expansion method express…
Algebraic structures and Hamiltonians from the equivalence classes of 2D conformal algebras
Ian Marquette, Junze Zhang, Yao-Zhong Zhang
The construction of superintegrable systems based on Lie algebras and their universal enveloping algebras has been widely studied over the past decades. However, most constructions…
Polynomial algebras from commutants: Classical and Quantum aspects of
Rutwig Campoamor-Stursberg, Danilo Latini, Ian Marquette +1
We review some aspects of the Racah algebra , including the closure relations, pointing out their role in superintegrability, as well as in the description of the symmetry al…