Generalized Deformed su(2) Algebras, Deformed Parafermionic Oscillators and Finite W Algebras

TL;DR

This paper explores the structure of generalized deformed su(2) algebras and their applications to various physical systems and mathematical frameworks, revealing new symmetries and algebraic connections.

Contribution

It identifies the algebraic structures underlying several physical systems and mathematical models, including generalized deformed su(2) algebras and finite W algebras, and links them to known representation theories.

Findings

Physical systems exhibit generalized deformed su(2) algebra structures.

The algebra of certain systems matches known mathematical algebras like finite W algebras.

The Holt potential is characterized by W$_3^{(2)}$ symmetry.

Abstract

Several physical systems (two identical particles in two dimensions, isotropic oscillator and Kepler system in a 2-dim curved space) and mathematical structures (quadratic algebra QH(3), finite W algebra $\bar {\rm W}_0$) are shown to posses the structure of a generalized deformed su(2) algebra, the representation theory of which is known. Furthermore, the generalized deformed parafermionic oscillator is identified with the algebra of several physical systems (isotropic oscillator and Kepler system in 2-dim curved space, Fokas--Lagerstrom, Smorodinsky--Winternitz and Holt potentials) and mathematical constructions (generalized deformed su(2) algebra, finite W algebras $\bar {\rm W}_0$ and W$_3^{(2)}$). The fact that the Holt potential is characterized by the W$_3^{(2)}$ symmetry is obtained as a by-product.