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

L. Frappat; A. Sciarrino; S. Sciuto; P. Sorba

doi:10.1088/0305-4470/30/3/015

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arXiv · q-alg/9609033

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

L. Frappat·A. Sciarrino·S. Sciuto·P. Sorba

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Abstract

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 $ν$ of the anyons by q = exp(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,N)) is obtained.

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L. Frappat, A. Sciarrino, S. Sciuto, P. Sorba. 1996-09-30. Anyonic Realization of the Quantum Affine Lie Superalgebra U_q(A(M,N)^{(1)}). https://doi.org/10.1088/0305-4470%2F30%2F3%2F015

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