85 citations · 273 across the 11 of their papers we have counts for
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Matrix equations and trilinear commutation relations
Sergey Klishevich
In this paper we discuss a general algebraic approach to treating static equations of matrix models with a mass-like term. In this approach the equations of motions are considered…
Quasi-exact solvability and intertwining relations
Sergey Klishevich
We emphasize intertwining relations as a universal tool in constructing one-dimensional quasi-exactly solvable operators and offer their possible generalization to the multidimensi…
Dolan-Grady Relations and Noncommutative Quasi-Exactly Solvable Systems
Sergey M. Klishevich, Mikhail S. Plyushchay
We investigate a U(1) gauge invariant quantum mechanical system on a 2D noncommutative space with coordinates generating a generalized deformed oscillator algebra. The Hamiltonian…
Nonlinear Holomorphic Supersymmetry on Riemann Surfaces
Sergey M. Klishevich, Mikhail S. Plyushchay
We investigate the nonlinear holomorphic supersymmetry for quantum-mechanical systems on Riemann surfaces subjected to an external magnetic field. The realization is shown to be po…
Nonlinear holomorphic supersymmetry, Dolan-Grady relations and Onsager algebra
Sergey M. Klishevich, Mikhail S. Plyushchay
Recently, it was noticed by us that the nonlinear holomorphic supersymmetry of order , (-HSUSY) has an algebraic origin. We show that the Onsager algebra underlies…
Nonlinear Supersymmetry
Sergey M. Klishevich, Mikhail S. Plyushchay
After a short discussion of the intimate relation between the generalized statistics and supersymmetry, we review the recent results on the nonlinear supersymmetry obtained in the…