arXiv:q-alg/9609033v1 30 Sep 1996 ANYONIC REALIZATION OF THE QUANTUM AFFINE LIE SUPERALGEBRAS U q (  A(M − 1,N − 1)) L. Frappat a 1 , A. Sciarrino b , S. Sciuto c , P. Sorba d a Centre de Recherches Math´ ematiques Universit´ e de Montr´ eal, Canada b Dipartimento di Scienze Fisiche, Universit` a di Napoli “Federico II” and I.N.F.N., Sezione di Napoli, Italy c Dipartimento di Fisica Teorica, Universit` a di Torino and I.N.F.N., Sezione di Torino, Italy d Laboratoire de Physique Th´ eorique ENSLAPP Annecy-le-Vieux et Lyon, France Abstract We give a realization of the quantum affine Lie superalgebras U q (  A(M − 1,N − 1)) in terms of anyons defined on a one or two-dimensional lattice, the deformation pa- rameter q being related to the statistical parameter ν of the anyons by q = e iπν . 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 − 1,N − 1)) is obtained. CRM-2383 DSF-T-35/96 DFTT-39/96 ENSLAPP-AL-603/96 q-alg/9609033 September 1996 1 On leave of absence from Laboratoire de Physique Th´ eorique ENSLAPP.