Regular representations of the group of finite upper-triangular matrices, corresponding to product measures, and criteria for their irreducibility (Q2722118)
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scientific article; zbMATH DE number 1617366
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Regular representations of the group of finite upper-triangular matrices, corresponding to product measures, and criteria for their irreducibility |
scientific article; zbMATH DE number 1617366 |
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11 July 2001
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infinite-dimensional group
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regular representation
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Gaussian measure
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Regular representations of the group of finite upper-triangular matrices, corresponding to product measures, and criteria for their irreducibility (English)
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The author defines and studies analogs of the regular representation for the group of finite upper-triangular matrices of infinite order (here ``finite'' means that each row of an infinite matrix contains a finite number of non-zero elements). The representations correspond to quasi-invariant product measures on the group of all upper-triangular matrices. Under some technical assumptions, a criterion of their irreducibility is given.
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