Anyonic Realization of the Quantum Affine Lie Algebra U_q(A_N)

L. Frappat (1) , A. Sciarrino , S. Sciuto , P. Sorba (1)

1 LAPTH - Laboratoire d'Annecy-le-Vieux de Physique Théorique

We give a realization of quantum affine Lie algebra $U_q(\hat A_{N-1})$ in terms of anyons defined on a two-dimensional lattice, the deformation parameter $q$ being related to the statistical parameter $\nu$ of the anyons by $q = e^{i\pi\nu}$. In the limit of the deformation parameter going to one we recover the Feingold-Frenkel fermionic construction of undeformed affine Lie algebra.

Domaines: Algèbres quantiques [math.QA]; Physique des Hautes Energies - Théorie [hep-th]

L. Frappat, A. Sciarrino, S. Sciuto, P. Sorba. Anyonic Realization of the Quantum Affine Lie Algebra U_q(A_N). Physics Letters B, 1996, 369, pp.313. ⟨hal-00350828⟩