GENERALIZED DEFORMED SU(2) ALGEBRAS, DEFORMED PARAFERMIONIC OSCILLATORS AND FINITE W-ALGEBRAS

Several physical systems (two identical particles in two dimensions, i sotropic oscillator and Kepler system in a two-dimensional curved spac e) and mathematical structures (quadratic algebra QH(3), finite W-alge bra ($) over bar W-o) are shown to possess the structure of a generali zed deformed su(2) algebra, the representation theory of which is know n. Furthermore, the generalized deformed parafermionic oscillator is i dentified with the algebra of several physical systems (isotropic osci llator and Kepler system in two-dimensional curved space, Fokas-Lagers trom, Smorodinsky-Winternitz and Holt, potentials) and mathematical co nstructions (generalized deformed su(2) algebra, finite W-algebras ($) over bar W-o and W-3((2))). The fact that the Holt potential is chara cterized by the W-3((2)) symmetry is obtained as a by-product.