REPRESENTATIONS OF THE GROUP OF DIFFEOMORPHISMS
REPRESENTATIONS OF THE GROUP OF DIFFEOMORPHISMS
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微分形群的表示
DOI：
10.1070/rm1975v030n06abeh001527
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发表时间：
1975
影响因子：
0.9
通讯作者：
M. Graev
中科院分区：
文献类型：
--
作者：
A. Vershik;I. Gel'fand;M. Graev
本文综述了与X中的构形空间（即局部有限子集空间）有关的非紧流形X的超同态群的表示的结果。这些表示是由ΓX上的一个拟不变测度μ构造的。特别地，建立了表示不可约的充分必要条件。在泊松测度μ的情况下，给出了相应的表示环的描述.
This article contains a survey of results on representations of the diffeomorphism group of a noncompact manifold X associated with the space ΓX of configurations (that is, of locally finite subsets) in X. These representations are constructed from a quasi-invariant measure μ on ΓX. In particular, necessary and sufficient conditions are established for the representations to be irreducible. In the case of the Poisson measure μ a description is given of the corresponding representation ring.