拓扑群的Poisson测度及其表示
Poisson measures for topological groups and their representations
摘要：
构造了群G上的高斯拟不变测度和环群G相对于稠密子群G'的高斯拟不变测度.在非阿基米德案例中，研究的措施类别比真实案例中更广泛。考虑了黎曼流形和非阿基米德流形的情形。本文研究了G'在$G^{\bf N}$上的与Poisson测度相关的酉表示，并利用了G上的拟不变测度.考虑了几个群体：（2）局部域上的非阿基米德流形的（a）超同态和（b）环群。除了这四种情形外，还考虑了第五种和第六种情形：（3）对于（a）实群和（b）非阿基米德群，研究了构形空间$Γ_M$上包含在流形乘积$M^{\bf N}$中的Poisson测度的Diff（M）表示.本文研究了无限维Banach流形M（3）（a），非Archimdean局部紧和非局部紧巴拿赫流形（3）（b）的情形.
英文摘要：
Gaussian quasi-invariant measures on groups of diffeomorphisms and loop groups G relative to dense subgroups G' were constructed. In the non-Archimedean case the wider class of measures was investigated, than in the real case. The cases of Riemann and non-Archimedean manifolds were considered. This article is related with unitary representations of G' associated with Poisson measures on $G^{\bf N}$ and uses quasi-invariant measures on G from the previous works. Several groups are considered: (1) (a) diffeomorphisms and (b) loop groups of real manifolds, (2) (a) diffeomorphisms and (b) loop groups of non-Archimedean manifolds over local fields. Besides these four cases further the fifth and the sixth cases are considered: for (3) (a) real and (b) non-Archimedean groups of diffeomorphisms Diff(M) representations associated with Poisson measures on configuration spaces $Γ_M$ contained in products of manifolds $M^{\bf N}$ are investigated. Here the cases of infinite-dimensional Banach manifold M (3) (a), non-Archimdean locally compact and non-locally compact Banach manifolds (3) (b) are investigated.
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