Fractional Spin Through Quantum Affine Algebra Aˆ(n) and Quantum Affine Super-algebra Aˆ(n, m)

摘要

Using the splitting of a Q-deformed boson, in the Q → q = e 2kπi limit, the fractionaldecomposition of the quantum affine algebra Aˆ(n) and the quantum affine super-algebra Aˆ(n, m)are found. This decomposition is based on the oscillator representation and can be related tothe fractional supersymmetry and k-fermionic spin. We establish also the equivalence betweenthe quantum affine algebra Aˆ(n) and the classical one in the fermionic realization.