Anyonic Realization of the Quantum Affine Lie Superalgebra U_q(A(M,N)^{(1)})

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 the quantum affine Lie superalgebras U_q(A(M,N))^(1) in terms of anyons defined on a one or two-dimensional lattice, the deformation parameter q being related to the statistical parameter $\nu$ of the anyons by q = exp(i\pi\nu). The construction uses anyons contructed from usual fermionic oscillators and deformed bosonic oscillators. As a byproduct, realization deformed in any sector of the quantum superalgebras U_q(A(M,N)) is obtained.

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 Superalgebra U_q(A(M,N)^{(1)}). Journal of Physics A General Physics (1968-1972), 1997, 30, pp.903. ⟨hal-00375848⟩