Fractional Spin through Quantum Affine Algebra $\hat{A}(n)$ and quantum affine superalgebra $\hat{A}(n,m)$

Abstract

Using the splitting of a $Q$-deformed boson, in the $Q\to q=e^{\frac{2\pi \mathrm{i}}{\mathrm{k}}}$ limit, the fractional decomposition of the quantum affine algebra $\hat{A}(n)$ and the quantum affine superalgebra $\hat{A}(n,m)$ are found. This decomposition is based on the oscillator representation and can be related to the fractional supersymmetry and k-fermionic spin. We establish also the equivalence between the quantum affine algebra $\hat{A}(n)$ and the classical one in the fermionic realization.

(17 pages, latex, non figures)