Vertex operators for quantum groups and application to integrable systems
E. Ragoucy
Abstract
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 UR in term of a deformed oscillators algebra AR. The realization we present is an infinite series, very similar to a vertex operator. Then, considering the integrable hierarchy naturally associated to AR, we show that UR 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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