Quantum Affine Algebras at Roots of Unity and Fractional Spin

We investigate the fractional decomposition of the quantum affine enveloping algebras UQ (A (n) ) and UQ (C (n) ) at the specialization Q q = e^2i{k}. Working within the bosonic Fock representation, we establish its connection to fractional supersymmetry and k-fermionic statistics, extending the standard fermionic/bosonic dichotomy to a Zₖ-graded framework. A central result is an explicit equivalence between these quantum affine algebras at roots of unity and their classical counterparts under fermionic realization. In this correspondence, the deformation parameter collapses while the representation-theoretic structure is preserved. The nilpotency conditions at Q = q are shown to enforce a truncation of the module content consistent with the k-fermionic picture.