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We review the notion of the deformation of the exterior wedge product. This allows us to construct the deformation of the algebra of exterior forms over a vector space and also over an arbitrary manifold. We relate this approach to the generalized statistics. we study quons, as a particular case of these generalized statistics. We also give their… (More)
A relation between the Z3-graded Grassmann variables and parafermions is established. Coherent states are constructed as a direct consequence of such a relationship. We also give the analog of the Bargmann-Fock representation in terms of these Grassmann variables.
We give a general approach for the construction of deformed oscillators. These ones could be seen as describing deformed bosons. Basing on new definitions of certain quantum series, we demonstrate that they are nothing but the ordinary exponential functions in the limit when the deformation parameters goes to one. We also prove that these series converge to… (More)
A generalized definition of a deformation of the fermionic oscillator (k-fermionic oscillators) is proposed. Two prescriptions for the construction of generalized Grass-mann coherent states for this kind of oscillators are derived. The two prescriptions differs in the nature of the generalized Grassmann variables used. While we use Majid's definition for… (More)
Generalized Z k-graded Grassmann variables are used to label coherent states related to the nilpotent representation of the q-oscillator of Biedenharn and Macfarlane when the deformation parameter is a root of unity. These states are then used to construct generalized Grassmann representatives of state vectors. Recently in  we have constructed coherent… (More)