Anyonic Realization of the Quantum Affine Lie Superalgebra Uq(A(M,N)(1))
Abstract
We give a realization of the quantum affine Lie superalgebras Uq(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 of the anyons by q = exp(iπ). 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 Uq(A(M,N)) is obtained.
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