On the Degenerate Whittaker space for some induced representations of ${\rm GL}_4(\mathfrak{o}_2)$
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| Format: | Preprint |
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2025
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| _version_ | 1866909736999321600 |
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| author | Parashar, Ankita Patel, Shiv Prakash |
| author_facet | Parashar, Ankita Patel, Shiv Prakash |
| contents | Let $\mathfrak{o}_l$ be a finite principal ideal local ring of length $l$. The degenerate Whittaker space associated with a representation of ${\rm GL}_{2n}(\mathfrak{o}_l)$ is a representation of ${\rm GL}_n(\mathfrak{o}_l)$. For strongly cuspidal representations of ${\rm GL}_{2n}(\mathfrak{o}_l)$ the structure of degenerate Whittaker space is described by Prasad's conjecture, which has been proven for ${\rm GL}_4(\mathfrak{o}_2)$. In this paper, we describe the degenerate Whittaker space for certain induced representations of ${\rm GL}_4(\mathfrak{o}_2)$, specifically those induced from subgroups analogous to the maximal parabolic subgroups of ${\rm GL}_4(\mathbb{F}_q)$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_10796 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Degenerate Whittaker space for some induced representations of ${\rm GL}_4(\mathfrak{o}_2)$ Parashar, Ankita Patel, Shiv Prakash Representation Theory Group Theory 20G25, 20G05, 20C15 Let $\mathfrak{o}_l$ be a finite principal ideal local ring of length $l$. The degenerate Whittaker space associated with a representation of ${\rm GL}_{2n}(\mathfrak{o}_l)$ is a representation of ${\rm GL}_n(\mathfrak{o}_l)$. For strongly cuspidal representations of ${\rm GL}_{2n}(\mathfrak{o}_l)$ the structure of degenerate Whittaker space is described by Prasad's conjecture, which has been proven for ${\rm GL}_4(\mathfrak{o}_2)$. In this paper, we describe the degenerate Whittaker space for certain induced representations of ${\rm GL}_4(\mathfrak{o}_2)$, specifically those induced from subgroups analogous to the maximal parabolic subgroups of ${\rm GL}_4(\mathbb{F}_q)$. |
| title | On the Degenerate Whittaker space for some induced representations of ${\rm GL}_4(\mathfrak{o}_2)$ |
| topic | Representation Theory Group Theory 20G25, 20G05, 20C15 |
| url | https://arxiv.org/abs/2508.10796 |