Elementary representations of the group \(B_0^\mathbb N\) of finite upper-triangular matrices (Q2754838)
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scientific article; zbMATH DE number 1668458
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Elementary representations of the group \(B_0^\mathbb N\) of finite upper-triangular matrices |
scientific article; zbMATH DE number 1668458 |
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4 November 2001
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elementary representation
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regular representation
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infinite-dimensional group
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Elementary representations of the group \(B_0^\mathbb N\) of finite upper-triangular matrices (English)
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The author introduces a family of representations (called ``elementary'') of the group \(B_0^\mathbb N\) of upper-triangular matrices infinite in one direction with a finite number of non-zero off-diagonal elements. A criterion of irreducibility and equivalence of these representations is given. Regular representations of \(B_0^\mathbb N\) studied earlier by the author [\textit{A. V. Kosyak}, Selecta Math. Sov. 11, 241-291 (1992; Zbl 0798.22008)] are shown to be infinite tensor products of elementary representations. In connection with that, conditions for the irreducibility of tensor products of elementary representations are found.
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