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A long-term research proposal on the algebraic structure, the representationsand the possible applications of paraparticle algebras is structured in threemodules: The first part stems from an attempt to classify the inequivalentgradings and braided group structures present in the various parastatisticalalgebraic models. The second part of the proposal aims at refining andutilizing a previously published methodology for the study of the Fock-likerepresentations of the parabosonic algebra, in such a way that it can also bedirectly applied to the other parastatistics algebras. Finally, in the thirdpart, a couple of Hamiltonians is proposed, and their sutability for modelingthe radiation matter interaction via a parastatistical algebraic model isdiscussed.

Gradings, Braidings, Representations, Paraparticles: some open problems