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On a class of representations of the Yangian and moduli space of monopoles | | A. Gerasimov
; S. Kharchev
; D. Lebedev
; S. Oblezin
; | | Date: |
2 Sep 2004 | | Subject: | Algebraic Geometry; Quantum Algebra | math.AG math.QA | | Abstract: | A new class of infinite dimensional representations of the Yangians $Y(frak{g})$ and $Y(frak{b})$ corresponding to a complex semisimple algebra $frak{g}$ and its Borel subalgebra $frak{b}subsetfrak{g}$ is constructed. It is based on the generalization of the Drinfeld realization of $Y(frak{g})$, $frak{g}=frak{gl}(N)$ in terms of quantum minors to the case of an arbitrary semisimple Lie algebra $frak{g}$. 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 $mathbb{P}^1$ into the generalized flag manifold $X=G/B$. Thus the constructed representations of the Yangian may be considered as a quantization of the moduli space of the monopoles. | | Source: | arXiv, math.AG/0409031 | | Services: | Forum | Review | PDF | Favorites | |
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