A nonabelian Fourier transform for tempered unipotent representations
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866929294600568832 |
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| author | Aubert, Anne-Marie Ciubotaru, Dan Romano, Beth |
| author_facet | Aubert, Anne-Marie Ciubotaru, Dan Romano, Beth |
| contents | We define an involution on the space of compact tempered unipotent representations of inner twists of a split simple $p$-adic group $G$ and investigate its behaviour with respect to restrictions to reductive quotients of maximal compact open subgroups. In particular, we formulate a precise conjecture about the relation with a version of Lusztig's nonabelian Fourier transform on the space of unipotent representations of the (possibly disconnected) reductive quotients of maximal compact subgroups. We give evidence of the conjecture, including proofs for $\mathsf{SL}_n$ and $\mathsf{PGL}_n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2106_13969 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | A nonabelian Fourier transform for tempered unipotent representations Aubert, Anne-Marie Ciubotaru, Dan Romano, Beth Representation Theory 22E50, 20C33 We define an involution on the space of compact tempered unipotent representations of inner twists of a split simple $p$-adic group $G$ and investigate its behaviour with respect to restrictions to reductive quotients of maximal compact open subgroups. In particular, we formulate a precise conjecture about the relation with a version of Lusztig's nonabelian Fourier transform on the space of unipotent representations of the (possibly disconnected) reductive quotients of maximal compact subgroups. We give evidence of the conjecture, including proofs for $\mathsf{SL}_n$ and $\mathsf{PGL}_n$. |
| title | A nonabelian Fourier transform for tempered unipotent representations |
| topic | Representation Theory 22E50, 20C33 |
| url | https://arxiv.org/abs/2106.13969 |