Generalized coherent states associated with the C_{\lambda}-extended oscillator

Two new types of coherent states associated with the C_{\lambda}-extended oscillator, where C_{\lambda} is the cyclic group of order \lambda, are introduced. The first ones include as special cases both the Barut-Girardello and the Perelomov su(1,1) coherent states for \lambda=2, as well as the annihilation-operator coherent states of the C_{\lambda}-extended oscillator spectrum generating algebra for higher \lambda values. The second ones, which are eigenstates of the C_{\lambda}-extended oscillator annihilation operator, extend to higher \lambda values the paraboson coherent states, to which they reduce for \lambda=2. All these states satisfy a unity resolution relation in the C_{\lambda}-extended oscillator Fock space (or in some subspace thereof). They give rise to Bargmann representations of the latter, wherein the generators of the C_{\lambda}-extended oscillator algebra are realized as differential-operator-valued matrices (or differential operators). The statistical and squeezing properties of the new coherent states are investigated over a wide range of parameters and some interesting nonclassical features are exhibited.