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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.15128 |
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| _version_ | 1866908704543080448 |
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| author | Bhattacharya, Sarbartha Chen, Tsao-Hsien |
| author_facet | Bhattacharya, Sarbartha Chen, Tsao-Hsien |
| contents | In this paper we give a description of the depth-$r$ Bernstein center for non-negative integers $r$ of a reductive simply connected group $G$ over a non-archimedean local field as a limit of depth-$r$ standard parahoric Hecke algebras. Using the description, we construct maps from the algebra of stable functions on the $r$-th Moy-Prasad filtration quotient of hyperspecial parahorics to the depth-$r$ Bernstein center and use them to attach to each depth-$r$ irreducible representation $π$ an invariant $θ(π)$, called the depth-$r$ Deligne-Lusztig parameter of $π$. We show that $θ(π)$ is equal to the semi-simple part of minimal $K$-types of $π$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_15128 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A description of the integral depth-$r$ Bernstein center Bhattacharya, Sarbartha Chen, Tsao-Hsien Representation Theory Number Theory In this paper we give a description of the depth-$r$ Bernstein center for non-negative integers $r$ of a reductive simply connected group $G$ over a non-archimedean local field as a limit of depth-$r$ standard parahoric Hecke algebras. Using the description, we construct maps from the algebra of stable functions on the $r$-th Moy-Prasad filtration quotient of hyperspecial parahorics to the depth-$r$ Bernstein center and use them to attach to each depth-$r$ irreducible representation $π$ an invariant $θ(π)$, called the depth-$r$ Deligne-Lusztig parameter of $π$. We show that $θ(π)$ is equal to the semi-simple part of minimal $K$-types of $π$. |
| title | A description of the integral depth-$r$ Bernstein center |
| topic | Representation Theory Number Theory |
| url | https://arxiv.org/abs/2407.15128 |