Moduli space of $G-$ monopoles, representations ofquantum groups and quantum integrable systems
We show that the moduli spaces of the $R^3$- monopoles for an arbitrary semisimple group are isomorphic to the symplectic leaves of the Yangian as symplectic manifolds. We quantize these symplectic leaves and construct corresponding representations of the Yangians in terms of the difference operators.
Thus we manage to quantize the moduli space of the monopoles using the quantum groups (Yangian). The application to quantum integrable systems will be explained. More precisely, the moduli space of monopoles produces a universal set of the separated variables to various integrable systems.
The talk is based on the common papers with A. Gerasimov, S. Kharchev, and S. Oblezin.
IHES, Bures sur Yvette
Speaker
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Dmitrii LEBEDEV
