What question did this study set out to answer?

The aim is to extend the understanding of reducibility in simple supercuspidal representations of symplectic groups within non-Archimedean local fields.

May 31, 2026Bulletin of the London Mathematical SocietyOpen Access

Reducibility points and characteristic p local fields I: simple supercuspidal representations of symplectic groups

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The aim is to extend the understanding of reducibility in simple supercuspidal representations of symplectic groups within non-Archimedean local fields.
Extended Mœglin's criterion for reducibility of representations in positive characteristic.
Utilized Langlands correspondence to analyze the transfer of supercuspidal representations.
Applied prior results from works concerning p-adic fields to non-Archimedean fields.
Established a clear relationship between reducibility of representations and g-factors for pairs.
Demonstrated that smooth irreducible representations are linked through the Langlands correspondence.
Provided explicit construction methods for simple representations based on Gross and Reeder's definitions.

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Implication

Describes a method to analyze reducibility in supercuspidal representations, enhancing Langlands correspondence for specific local fields.

Cite This Study

Blondel et al. (2026) studied this question.

synapsesocial.com/papers/6a1bd12d5783ba022b6fcbb6 https://doi.org/10.1112/blms.70389

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Implication

Describes a method to analyze reducibility in supercuspidal representations, enhancing Langlands correspondence for specific local fields.

Reducibility points and characteristic p local fields I: simple supercuspidal representations of symplectic groups

Key Points

Discussion

Implication

Cite This Study

Reducibility points and characteristic p local fields I: simple supercuspidal representations of symplectic groups

Key Points

Discussion

Implication

Cite This Study

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