On a Class of Representations of Quantum Groups
On a Class of Representations of Quantum Groups
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论量子群的一类表示
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
S. Oblezin
中科院分区：
文献类型：
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作者：
A. Gerasimov;S. Kharchev;D. Lebedev;S. Oblezin
本文简要说明了量子组的新类无限尺寸表示形式的构建。示例包括有限维量子组$ u_q（Mathfrak {g}）$，Yangian $ y（Mathfrak {G}）$和零级别的Aggine量子组
$ u_q（HAT {MATHFRAK {G}}）_ {C = 0} $对应于任意有限的二维半密码lie lie algebra $ mathfrak {g} $。在中间步骤，我们将量子基团嵌入到量子多维圆环上的有理函数的代数中。本文中使用的量子组的显式参数化与单极的模量空间的参数化密切相关。结果，该表示形式的拟议构造提供了$ rr^3 $和$ rr^2 imes s^1 $的单极模量空间的量化。
This paper is a short account of the construction of a new class of the infinite-dimensional representations of the quantum groups. The examples include finite-dimensional quantum groups $U_q(mathfrak{g})$, Yangian $Y(mathfrak{g})$ and affine quantum groups at zero level
$U_q(hat{mathfrak{g}})_{c=0}$ corresponding to an arbitrary finite-dimensional semisimple Lie algebra $mathfrak{g}$. At the intermediate step we construct the embedding of the quantum groups into the algebra of the rational functions on the quantum multi-dimensional torus. The explicit parameterization of the quantum groups used in this paper turns out to be closely related to the parameterization of the moduli spaces of the monopoles. As a result the proposed constructions of the representations provide a quantization of the moduli spaces of the monopoles on $RR^3$ and $RR^2 imes S^1$.
DOI：
10.1515/9781400859306
发表时间：
1988
期刊：
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影响因子：
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作者：
M. Atiyah;N. Hitchin
通讯作者：
M. Atiyah;N. Hitchin