Fractional spin through quantum affine algebras with vanishing central charge

In this paper, we study the fractional decomposition of the quantum enveloping affine algebras $U_Q(\hat A(n))$ and $U_Q(\hat{C}(n))$ with vanishing central charge in the limit $Q\to q=e^{\frac{2iπ}k}$ . This decomposition is based on the bosonic representation and can be related to the fractional supersymmetry and $k$-fermionic spin. The equivalence between the quantum affine algebras and the classical ones in the fermionic realization is also established.

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