Generalized Coherent States Associated with the $C_{\lambda}$-Extended Oscillator

Abstract

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. They satisfy a unity resolution relation in the $C_{\lambda}$-extended oscillator Fock space (or in some subspace thereof) and 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.