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Australasian Research Symposium on Lie Groups, Algebraic Groups, Quantum Groups, and Their Representations (LAQ'2001)
December 7-10, 2001
The University of Auckland
Auckland, New Zealand

Organizers
Rod Gover (University of Auckland), Vladimir Pestov (Victoria University of Wellington)

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Quantum groups symmetry in integrable systems with or without boundary
by
E. Ragoucy
LAPTH (CNRS, France)

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.

The same procedure is then applied to the case with boundary, where the deformed oscillators algebra is replaced to a so-called boundary algebra. In particular, we prove that this bundary algebra can be embbeded into a deformed oscillators algebra.

Paper reference: arXiv:math.QA/0108207, arXiv:math.QA/0108221

Date received: October 31, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cahw-17.