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The central aim is to explore the fractional decomposition of quantum affine algebras at roots of unity.

May 6, 2026Open Access

Quantum Affine Algebras at Roots of Unity and Fractional Spin

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The central aim is to explore the fractional decomposition of quantum affine algebras at roots of unity.
Analyzing $U_Q(\hat{A}(n))$ and $U_Q(\widehat{C}(n))$ at the specialization $Q \rightarrow q = e^{\frac{2i\pi}{k}}$
Employing the bosonic Fock representation
Establishing a connection to fractional supersymmetry and $k$-fermionic statistics
Establishes equivalence between quantum affine algebras at roots of unity and classical counterparts
Shows preservation of representation-theoretic structure while the deformation parameter collapses
Demonstrates nilpotency conditions enforce truncation consistent with the $k$-fermionic picture

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This investigation establishes connections between quantum affine algebras, fractional supersymmetry, and k-fermionic statistics.

Mostafa Mansour (2004) studied this question.

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