$U_q(\hat{\frak{gl}}_{{}_N})$ action on $\hat{\frak{gl}}_{{}_N}$ -modules and quantum toroidal algebras

Details $U_q(\hat{\frak{gl}}_{{}_N})$ action on $\hat{\frak{gl}}_{{}_N}$ -modules and quantum toroidal algebras $U_q(\hat{\frak{gl}}_{{}_N})$ action on $\hat{\frak{gl}}_{{}_N}$ -modules and quantum toroidal algebras

2002-02-27

arxiv.org/abs/math/0202292v1

J. Algebra 273 (2004), no. 1, 320--343.

Mathematics

Quantum Algebra

23 pages

Scientific paper

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 $gl_n$ and show that the simple generators give rise a realization of the quantum toroidal algebra with two parameters.

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