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This is a Quantitative Study study.

October 19, 2025Open Access

Parametrization of supercuspidal representations of depth zero for some simple adjoint groups

Key Points

A surjective map connects depth-zero L-parameters with representations, ensuring accurate classification.
The study verifies bijectivity for various cases, enhancing understanding of representation theory.
The Hiraga-Ichino-Ikeda conjecture holds for this parametrization if bijective connections are established.
This research sheds light on the relationship between L-parameters and irreducible representations, influencing future studies.

Abstract

We construct a surjective map from the set of conjugacy classes of depth-zero cuspidal enhanced L-parameters to that of isomorphism classes of depth-zero supercuspidal representations for simple adjoint groups, and check the bijectivity in various cases. We also prove that the Hiraga--Ichino--Ikeda conjecture on the formal degree of essentially square-integrable irreducible representations holds for this parametrization if it is bijective.

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Cite This Study

Atsushi Fujii (Wed,) studied this question.

synapsesocial.com/papers/68f43f92854d1061a58acb25 https://doi.org/https://doi.org/10.48550/arxiv.2504.17225

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