Irreducibility of regular Gaussian representations of the group \(B_0^\mathbb Z\) (Q2754852)
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scientific article; zbMATH DE number 1668470
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Irreducibility of regular Gaussian representations of the group \(B_0^\mathbb Z\) |
scientific article; zbMATH DE number 1668470 |
Statements
4 November 2001
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regular representation
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infinite-dimensional group
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Gaussian measure
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0.9176524
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0.88907695
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0.8863964
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0.88295066
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0.8790316
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0.87608016
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Irreducibility of regular Gaussian representations of the group \(B_0^\mathbb Z\) (English)
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The author defines the notion of regular representation for the group \(B_0^\mathbb Z\) of such upper-triangular matrices infinite in both directions and such that only a finite number of off-diagonal elements of each matrix is different from zero. The regular representation acts on the group of all upper-triangular matrices with a quasi-invariant Gaussian measure. Sufficient conditions for the irreducibility of the regular representation are given. The case of the group of upper-triangular matrices infinite in one direction was considered by the author earlier [see \textit{A. V. Kosyak}, Selecta Math. Sov. 11, 241-291 (1992; Zbl 0798.22008)].
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