Abstract
A new class of infinite dimensional representations of the Yangians Y
and Y
corresponding to a complex semisimple algebra 
and its Borel subalgebra 
is constructed. It is based on the generalization of the Drinfeld realization of 
in terms of quantum minors to the case of an arbitrary semisimple Lie algebra . The Poisson geometry associated with the constructed representations is described. In particular it is shown that the underlying symplectic leaves are isomorphic to the moduli spaces of G-monopoles defined as the components of the space of based maps of ℙ1 into the generalized flag manifold 
. Thus the constructed representations of the Yangian may be considered as a quantization of the moduli space of the monopoles.
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Gerasimov, A., Kharchev, S., Lebedev, D. et al. On a Class of Representations of the Yangian and Moduli Space of Monopoles. Commun. Math. Phys. 260, 511–525 (2005). https://doi.org/10.1007/s00220-005-1417-3
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DOI: https://doi.org/10.1007/s00220-005-1417-3