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arXiv · 2510.07391

A depth-zero principal-series block whose Hecke algebra has a non-trivial two-cocycle

Jeffrey D. Adler·Jessica Fintzen·Kazuma Ohara
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Abstract

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.

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Jeffrey D. Adler, Jessica Fintzen, Kazuma Ohara. 2025-10-08. A depth-zero principal-series block whose Hecke algebra has a non-trivial two-cocycle. https://arxiv.org/abs/2510.07391

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