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| Format: | Preprint |
| Published: |
2024
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| Online Access: | https://arxiv.org/abs/2407.12199 |
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| _version_ | 1866916327965327360 |
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| author | Movchan, Evgenii |
| author_facet | Movchan, Evgenii |
| contents | We consider the problem of constructing a Gelfand--Tsetlin basis in irreducible representations of an infinite-dimensional general linear group. For a finite-dimensional irreducible representation of a general linear group, all elements of the Gelfand--Tsetlin basis are parameterized by Gelfand--Tsetlin schemes. We extend this definition to infinite Gelfand--Tsetlin schemes, which in turn parameterize elements of the Gelfand--Tsetlin basis of an irreducible representation of an infinite-dimensional complete linear group. Using the properties of colimits of representations with the highest weight, we present an explicit form of the Gelfand--Tsetlin basis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_12199 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Gelfand-Tsetlin basis for irreducible representations of an infinite-dimensional general linear group Movchan, Evgenii Representation Theory Group Theory We consider the problem of constructing a Gelfand--Tsetlin basis in irreducible representations of an infinite-dimensional general linear group. For a finite-dimensional irreducible representation of a general linear group, all elements of the Gelfand--Tsetlin basis are parameterized by Gelfand--Tsetlin schemes. We extend this definition to infinite Gelfand--Tsetlin schemes, which in turn parameterize elements of the Gelfand--Tsetlin basis of an irreducible representation of an infinite-dimensional complete linear group. Using the properties of colimits of representations with the highest weight, we present an explicit form of the Gelfand--Tsetlin basis. |
| title | The Gelfand-Tsetlin basis for irreducible representations of an infinite-dimensional general linear group |
| topic | Representation Theory Group Theory |
| url | https://arxiv.org/abs/2407.12199 |