Comparing Bushnell-Kutzko and Sécherre's constructions of types for $\mathrm{GL}_{N}$ and its inner forms with Yu's construction
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| Format: | Preprint |
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2021
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| _version_ | 1866916305874976768 |
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| author | Mayeux, Arnaud Yamamoto, Yuki |
| author_facet | Mayeux, Arnaud Yamamoto, Yuki |
| contents | Let $F$ be a non-archimedean local field, $A$ be a central simple $F$-algebra, and $G$ be the multiplicative group of $A$. To construct types for supercuspidal representations of $G$, simple types by Sécherre and Yu's construction are already known. In this paper, we compare these constructions. In particular, we show essentially tame supercuspidal representations of $G$ defined by Bushnell-Henniart are nothing but tame supercuspidal representations defined by Yu. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_12367 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Comparing Bushnell-Kutzko and Sécherre's constructions of types for $\mathrm{GL}_{N}$ and its inner forms with Yu's construction Mayeux, Arnaud Yamamoto, Yuki Representation Theory Number Theory 11F70, 11S37, 20G05, 20G25, 22E50 Let $F$ be a non-archimedean local field, $A$ be a central simple $F$-algebra, and $G$ be the multiplicative group of $A$. To construct types for supercuspidal representations of $G$, simple types by Sécherre and Yu's construction are already known. In this paper, we compare these constructions. In particular, we show essentially tame supercuspidal representations of $G$ defined by Bushnell-Henniart are nothing but tame supercuspidal representations defined by Yu. |
| title | Comparing Bushnell-Kutzko and Sécherre's constructions of types for $\mathrm{GL}_{N}$ and its inner forms with Yu's construction |
| topic | Representation Theory Number Theory 11F70, 11S37, 20G05, 20G25, 22E50 |
| url | https://arxiv.org/abs/2112.12367 |