  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.
