On a class of representations of quantum groups

被引:0
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作者
Gerasimov, A [1 ]
Kharchev, S
Lebedev, D
Oblezin, S
机构
[1] Moscow Theoret & Expt Phys Inst, Moscow 117259, Russia
[2] Univ Dublin Trinity Coll, Dept Pure & Appl Math, Dublin 2, Ireland
[3] TCD, Hamilton Math Inst, Dublin 2, Ireland
[4] Max Planck Inst Math, D-53111 Bonn, Germany
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中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
This paper is a short account of the construction of a new class of infinite-dimensional representations of the quantum groups. The examples include finite-dimensional quantum groups U-q(q), Yangians Y(g) and affine quantum groups at zero level U-q((g) over cap)(c=0) corresponding to an arbitrary finite-dimensional semisimple Lie algebra g. At an intermediate step we construct an embedding of the quantum groups into the algebra of 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 monopoles. As a result the proposed constructions of the representations provide a quantization of the moduli spaces of monopoles on R-3 and R-2 x S-1.
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页码:101 / 110
页数:10
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