Distinction of the Steinberg representation and the dual group of a symmetric space
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910066811076608 |
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| author | Shtotland, Guy |
| author_facet | Shtotland, Guy |
| contents | We study the distinction of the Steinberg representation of a split reductive group $G$ with respect to a split symmetric subgroup $H \subset G$. We relate this distinction problem to a problem about the existence of a non-zero harmonic function on a certain hyper-graph related to $X = G/H$. We verify the relative local Langlands conjecture for the Steinberg representation by showing that over a $p$-adic field the Steinberg representation is $H$-distinguished if and only if its Langlands parameter factors through the dual group of $X$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_01701 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Distinction of the Steinberg representation and the dual group of a symmetric space Shtotland, Guy Representation Theory 22E50, 20C33 We study the distinction of the Steinberg representation of a split reductive group $G$ with respect to a split symmetric subgroup $H \subset G$. We relate this distinction problem to a problem about the existence of a non-zero harmonic function on a certain hyper-graph related to $X = G/H$. We verify the relative local Langlands conjecture for the Steinberg representation by showing that over a $p$-adic field the Steinberg representation is $H$-distinguished if and only if its Langlands parameter factors through the dual group of $X$. |
| title | Distinction of the Steinberg representation and the dual group of a symmetric space |
| topic | Representation Theory 22E50, 20C33 |
| url | https://arxiv.org/abs/2501.01701 |