Vertex operators for quantum groups and application to integrable systems

Details Vertex operators for quantum groups and application to integrable systems Vertex operators for quantum groups and application to integrable systems

2001-08-30

arxiv.org/abs/math/0108207v2

J.Phys.A35:7929-7942,2002

Mathematics

Quantum Algebra

19 pages, no figure, Latex2e Error in theorem 3.3 and lemma 3.1 corrected

Scientific paper

10.1088/0305-4470/35/37/305

Starting with any R-matrix with spectral parameter, obeying the Yang-Baxter equation and a unitarity condition, we construct the corresponding infinite dimensional quantum group U_{R} in term of a deformed oscillators algebra A_R. The realization we present is an infinite series, very similar to a vertex operator. Then, considering the integrable hierarchy naturally associated to A_{R}, we show that U_{R} provides its integrals of motion. The construction can be applied to any infinite dimensional quantum group, e.g. Yangians or elliptic quantum groups. Taking as an example the R-matrix of Y(N), the Yangian based on gl(N), we recover by this construction the nonlinear Schrodinger equation and its Y(N) symmetry.

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