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October 2, 2025Open Access

On parameters of Hecke algebras for p-adic groups

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The affine Hecke algebra attached to depth-zero types can be computed explicitly, enhancing our understanding of their parameters.
An isomorphism between the affine Hecke algebra for depth-zero types and the one for unipotent types is established.
A conjecture by Lusztig regarding the agreement of parameters across Bernstein blocks is confirmed under specific conditions.
The results have implications for the structure of Hecke algebras in relation to p-adic groups and their symmetries.

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This paper shows that Hecke algebras linked to depth-zero types are isomorphic to unipotent types, suggesting key interactions.

Kazuma Ohara (2025) studied this question.

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