The asymptotic Plancherel formula and Lusztig's asymptotic algebra for $\tilde{\mathsf{A}}_n$
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912976764665856 |
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| author | Chapelier-Laget, Nathan Guilhot, Jérémie Little, Eloise Parkinson, James |
| author_facet | Chapelier-Laget, Nathan Guilhot, Jérémie Little, Eloise Parkinson, James |
| contents | The aim of this paper is to give a new explicit construction of Lusztig's asymptotic algebra in affine type $\mathsf{A}$. To do so, we construct a balanced system of cell modules, prove an asymptotic version of the Plancherel Theorem and develop a relative version of the Satake Isomorphism for each two-sided Kazhdan-Lusztig cell. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_07004 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The asymptotic Plancherel formula and Lusztig's asymptotic algebra for $\tilde{\mathsf{A}}_n$ Chapelier-Laget, Nathan Guilhot, Jérémie Little, Eloise Parkinson, James Representation Theory The aim of this paper is to give a new explicit construction of Lusztig's asymptotic algebra in affine type $\mathsf{A}$. To do so, we construct a balanced system of cell modules, prove an asymptotic version of the Plancherel Theorem and develop a relative version of the Satake Isomorphism for each two-sided Kazhdan-Lusztig cell. |
| title | The asymptotic Plancherel formula and Lusztig's asymptotic algebra for $\tilde{\mathsf{A}}_n$ |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2406.07004 |