Fractional spin through quantum affine algebras with vanishing central charge

TL;DR

This paper explores the fractional decomposition of quantum affine algebras with zero central charge at roots of unity, linking it to fractional supersymmetry and classical algebra representations.

Contribution

It introduces a bosonic representation-based fractional decomposition of quantum affine algebras at roots of unity, connecting to fractional supersymmetry.

Findings

Fractional decomposition of quantum affine algebras established.

Relation to fractional supersymmetry and k-fermionic spin demonstrated.

Equivalence between quantum and classical affine algebras shown.

Abstract

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 $Q\to q=e^{\frac{2i\pi}k}$ . 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.