Anyonic realization of the quantum affine Lie algebra

1995/11/02 by L. Frappat, A. Sciarrino, S. Sciuto +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Random Matrices and Applications #hep-th #math.QA #q-alg

paper · pdf · doi:10.1016/0370-2693(95)01518-3

published as Phys.Lett.B369:313-324,1996 · 13p LaTeX Document (should be run twice)

arxiv created 1995/11/02 · openalex publication_date 1996/02/01 · arxiv updated 2009/11/30 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

We give a realization of quantum affine Lie algebra U_q( A_N-1) in terms of anyons defined on a two-dimensional lattice, the deformation parameter q being related to the statistical parameter ν of the anyons by q = e^iπν. In the limit of the deformation parameter going to one we recover the Feingold-Frenkel fermionic construction of undeformed affine Lie algebra.

Citations

• Q-analogues of Clifford and Weyl algebras-spinor and oscillator representations of quantum enveloping algebras
• Quantum Mechanics of Fractional-Spin Particles

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• Detailed balance and intermediate statistics