On a Class of Representations of the Yangian and Moduli Space of Monopoles
On a Class of Representations of the Yangian and Moduli Space of Monopoles
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论单极子杨格空间和模空间的一类表示
DOI：
10.1007/s00220-005-1417-3
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发表时间：
2004
影响因子：
2.4
通讯作者：
S. Oblezin
中科院分区：
文献类型：
--
作者：
A. Gerasimov;S. Kharchev;D. Lebedev;S. Oblezin
构造了一类新的Yangians Y和Y的无穷维表示，它们对应于复半单代数及其Borel子代数。它是基于推广的Drinfeld实现的量子未成年人的情况下，任意半单李代数。描述了与构造的表示相关联的泊松几何。特别是它表明，基本辛叶同构的G-单极定义为空间的组件的基础映射到广义旗流形的空间。因此，所构造的Yangian表示可以被认为是单极子的模空间的量子化。
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.
DOI：
10.1515/9781400859306
发表时间：
1988
期刊：
--
影响因子：
--
作者：
M. Atiyah;N. Hitchin
通讯作者：
M. Atiyah;N. Hitchin