A depth-zero principal-series block whose Hecke algebra has a non-trivial two-cocycle
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908583444086784 |
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| author | Adler, Jeffrey D. Fintzen, Jessica Ohara, Kazuma |
| author_facet | Adler, Jeffrey D. Fintzen, Jessica Ohara, Kazuma |
| contents | Recently the authors have shown that every Hecke algebra associated to a type constructed by Kim and Yu is isomorphic to a Hecke algebra for a depth-zero type. An example in the literature has been suggested as a counterexample to this result. We show that the example is not a counterexample, and exhibit some of its interesting properties, e.g., we show that a principal series, depth-zero type can have a Hecke algebra with non-trivial two-cocyle, a phenomenon that many did not expect could occur. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_07391 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A depth-zero principal-series block whose Hecke algebra has a non-trivial two-cocycle Adler, Jeffrey D. Fintzen, Jessica Ohara, Kazuma Representation Theory Number Theory Recently the authors have shown that every Hecke algebra associated to a type constructed by Kim and Yu is isomorphic to a Hecke algebra for a depth-zero type. An example in the literature has been suggested as a counterexample to this result. We show that the example is not a counterexample, and exhibit some of its interesting properties, e.g., we show that a principal series, depth-zero type can have a Hecke algebra with non-trivial two-cocyle, a phenomenon that many did not expect could occur. |
| title | A depth-zero principal-series block whose Hecke algebra has a non-trivial two-cocycle |
| topic | Representation Theory Number Theory |
| url | https://arxiv.org/abs/2510.07391 |