A polynomial class of u(2) algebras

Abstract

A r-parameter u({kappa 1, kappa 2,...,kappa r})(2) algebra is introduced. Finite unitary representations are investigated. This polynomial algebra reduces via a contraction procedure to the generalized Weyl-Heisenberg algebra A{.1,.2,...,.r} [M. Daoud and M. Kibler, J. Phys. A: Math. Theor. 45 (2012) 244036]. A pair of nonlinear (quadratic) bosons of type A(kappa) = A({kappa 1=kappa,kappa 2=0,...,.kappa r=0}) is used to construct, ` a la Schwinger, a one parameter family of (cubic) u(kappa)(2) algebra. The corresponding Hilbert space is constructed. The analytical Bargmann representation is also presented.