Two new types of coherent states associated with the $C_��$-extended oscillator, where $C_��$ is the cyclic group of order $��$, are introduced. They satisfy a unity resolution relation in the $C_��$-extended oscillator Fock space (or in some subspace thereof) and give rise to Bargmann representations of the latter, wherein the generators of the $C_��$-extended oscillator algebra are realized as differential-operator-valued matrices.

7 pages, LaTeX2e, no figure, communication at 2nd International Symposium Quantum Theory and Symmetries, Krakow, 18-21 July, 2001