Schubert cells and Whittaker functionals for $\text{GL}(n,\mathbb{R})$ part I: Combinatorics
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866917875898384384 |
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| author | Kim, Doyon |
| author_facet | Kim, Doyon |
| contents | We give a formula for a birational map on the Schubert cell associated to each Weyl group element of $G=\text{GL}(n)$. The map simplifies the UDL decomposition of matrices, providing structural insight into the Schubert cell decomposition of the flag variety $G/B$, where $B$ is a Borel subgroup. An application of the formula includes a new proof of the existence of Whittaker functionals for principal series representations of $\text{GL}(n,\mathbb{R})$ via integration by parts. In this paper, we establish combinatorial properties of the birational map and prove auxiliary results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_13519 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Schubert cells and Whittaker functionals for $\text{GL}(n,\mathbb{R})$ part I: Combinatorics Kim, Doyon Representation Theory Number Theory 11F70 (Primary), 05E14 (Secondary) We give a formula for a birational map on the Schubert cell associated to each Weyl group element of $G=\text{GL}(n)$. The map simplifies the UDL decomposition of matrices, providing structural insight into the Schubert cell decomposition of the flag variety $G/B$, where $B$ is a Borel subgroup. An application of the formula includes a new proof of the existence of Whittaker functionals for principal series representations of $\text{GL}(n,\mathbb{R})$ via integration by parts. In this paper, we establish combinatorial properties of the birational map and prove auxiliary results. |
| title | Schubert cells and Whittaker functionals for $\text{GL}(n,\mathbb{R})$ part I: Combinatorics |
| topic | Representation Theory Number Theory 11F70 (Primary), 05E14 (Secondary) |
| url | https://arxiv.org/abs/2410.13519 |