$U_q(\hat{\frak{gl}}_{{}_N})$ action on $\hat{\frak{gl}}_{{}_N}$ -modules and quantum toroidal algebras
Quantum Algebra
2020-09-08 v1
Abstract
We construct a vertex representation for the quantum toroidal algebra through the quantum general linear algebra. Using a new realization of the quantum general linear algebra we construct vertex operators for root vectors on the basic representation of the affine Lie algebra and show that the simple generators give rise a realization of the quantum toroidal algebra with two parameters.
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Cite
@article{arxiv.math/0202292,
title = {$U_q(\hat{\frak{gl}}_{{}_N})$ action on $\hat{\frak{gl}}_{{}_N}$ -modules and quantum toroidal algebras},
author = {Yun Gao and Naihuan Jing},
journal= {arXiv preprint arXiv:math/0202292},
year = {2020}
}
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23 pages