On degenerate Whittaker space for $GL_4(\mathfrak{o}_2)$
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913453638156288 |
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| author | Parashar, Ankita Patel, Shiv Prakash |
| author_facet | Parashar, Ankita Patel, Shiv Prakash |
| contents | Let $\mathfrak{o}_2$ be a finite principal ideal local ring of length 2. For a representation $π$ of $GL_{4}(\mathfrak{o}_2)$, the degenerate Whittaker space $π_{N, ψ}$ is a representation of $GL_2(\mathfrak{o}_2)$. We describe $π_{N, ψ}$ explicitly for an irreducible strongly cuspidal representation $π$ of $GL_4(\mathfrak{o}_2)$. This description verifies a special case of a conjecture of Prasad. We also prove that $π_{N, ψ}$ is a multiplicity free representation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_21165 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On degenerate Whittaker space for $GL_4(\mathfrak{o}_2)$ Parashar, Ankita Patel, Shiv Prakash Representation Theory 20G25, 20G05, 20C15 Let $\mathfrak{o}_2$ be a finite principal ideal local ring of length 2. For a representation $π$ of $GL_{4}(\mathfrak{o}_2)$, the degenerate Whittaker space $π_{N, ψ}$ is a representation of $GL_2(\mathfrak{o}_2)$. We describe $π_{N, ψ}$ explicitly for an irreducible strongly cuspidal representation $π$ of $GL_4(\mathfrak{o}_2)$. This description verifies a special case of a conjecture of Prasad. We also prove that $π_{N, ψ}$ is a multiplicity free representation. |
| title | On degenerate Whittaker space for $GL_4(\mathfrak{o}_2)$ |
| topic | Representation Theory 20G25, 20G05, 20C15 |
| url | https://arxiv.org/abs/2407.21165 |