Anyonic Realization of the Quantum Affine Lie Algebras
Frappat, L. ; Sciarrino, A. ; Sciuto, S. ; Sorba, P.
HAL, hal-00376654 / Harvested from HAL
Text on HAL
We give a realization of the quantum affine Lie algebras ${\cal U}_q(A_N^{(1)})$ and ${\cal U}_q(C_N^{(1)})$ in terms of anyons defined on a one-dimensional chain (or on a two-dimensional lattice), the deformation parameter $q$ being related to the statistical parameter $\nu$ of the anyons by $q = e^{i\pi\nu}$. In the limit of the deformation parameter going to one we recover the Feingold-Frenkel fermionic construction of undeformed affine Lie algebras.
Publié le : 1997-07-05
Classification:  [MATH.MATH-QA]Mathematics [math]/Quantum Algebra [math.QA],  [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th] 
@article{hal-00376654,
     author = {Frappat, L. and Sciarrino, A. and Sciuto, S. and Sorba, P.},
     title = {Anyonic Realization of the Quantum Affine Lie Algebras},
     journal = {HAL},
     volume = {1997},
     number = {0},
     year = {1997},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00376654}
}

Frappat, L.; Sciarrino, A.; Sciuto, S.; Sorba, P. Anyonic Realization of the Quantum Affine Lie Algebras. HAL, Tome 1997 (1997) no. 0, . http://gdmltest.u-ga.fr/item/hal-00376654/